Richiez: Question 2 is by Quiz master Doubledx


Provide just the answer in 10mins!!!

If f(x) = Sec(x), which of the following statement(s) is true?

1. f(x) = 1/cos(x)
2. f(x) = 1/{2cos^2(x/2) - 1}
3. f(x) = 1/{1 - 2sin^2(x/2)}

(remember more than one of the statements above could be right)

==========================
Solution to Question 2.
==========================

Since Sec(x) = 1/Cos(x),
Statement 1 is true...
Statement 2, Sec(x) = 1/{2cos²(x/2) - 1}
In this case we check it from the denominator of the expression =>
1/Cos(x)

Cos(x) = Cos(x/2 + x/2)

Applying trig identities for cos(A + B) = CosACosB - SinASinB,

We have =>

cos(x) = Cos(x/2)Cos(x/2) - sin(x/2)sin(x/2)
Cos(x) = cos²(x/2) - sin²(x/2).....(1)

But from trig identities=> sin²(A) + Cos²(A) = 1

Similarly=> sin²(x/2) + cos²(x/2) = 1
Thus=> sin²(x/2) = 1 - cos²(x/2)....(2)

Now, substituting (2) in (1) yields =>

Cos(x) = cos²(x/2) - [1 - cos²(x/2)]
Cos(x) = cos²(x/2) - 1 + cos²(x/2)

Colecting like terms yields =>

Cos(x) = 2cos²(x/2) - 1,
Now, since cosx = the denominator of statement 2 it means that it is true for Sec(x) = 1/Cos(x) = 2cos²(x/2) - 1

Now, to statement 3. the relationship is the same, it's only that this time we MUST solve in terms of sin(x) since the denominator is => {1 - 2sin²(x/2)}

Now we have to show that cos(x) = {1 - 2sin²(x/2)} to prove that the statement f(x) = sec(x) = 1/{1 - 2sin²(x/2)} is true.

Since from (1) above we know that =>

Cos(x) = cos²(x/2) - sin²(x/2).....(1)
And from trig identities
sin²(x/2) = 1 - cos²(x/2)....(2)

In this case we have to make cos²(x/2) the subject of the formula

Thus => cos²(x/2) = 1 - sin²(x/2)....(3)

which when you substitute (3) into (1) will yield=>

cos(x) = 1 - sin²(x/2) - sin²(x/2)
cos(x) = 1 - 2sin²(x/2)

Therefore since the denominator of statement 3 equals cos(x), it means...

1, 2 and 3 are all true, hence the solution. C is the correct Answer!

Note, this is not supposed to be this long but I had to explain for the benefit of other viewers!

SCORE CARD FOR ROUND 3 1st Question

1. :::JARYEH::: 10pts

2. :::DENNIECE1::: 10pts

3. :::IDENYIJOSHUA::: 8pts

4. :::PAPINDINHO::: 2pts

5. :::DR.GBOY::: 8pts

6. :::FACTORIAL1::: 8pts

7. :::AYSUCCESS99::: 10pts

8. :::MIRACY::: 2pts

9. :::KENDZYMA::: 10pts

10. :::LOGODWHIZ::: 8pts

11. [url=https://www.nairaland.com/amazing%20angel]:::AMAZING ANGEL:::[/url] 10pts

12. :::SMURFY::: 8pts

13. :::MOZARINIA::: 2pts

14. :::TOIDEVE::: 4pts

15. :::CASHIO::: 2pts

16. :::DYSHOW::: 4pts

participants should note that they are not allowed to post an answer twice....henceforth, double post will attract minus 1 mark

Alpha Maximus: Please post your answers to both Doubledx and me. And no double-answering please; cross-check before sending.

Yeah. No double answers, but remember option c was initially wrong.

get ready for Question 4 chosen by Busuyem

Question 4 ...still by Quiz master Doubledx

If the roots of the quadratic expression x^2 + Qx + 24 = 0 are α and ß respectively and the sum of their squares is 73, which of the following MUST be true about the values of x?

1. (x^2 + 3) > 10
2. (2x - 3) < 0
3. x^2 > 120

(remember, more than one option may be the correct answer)

just 10 mins!!! time is ticking

Richiez: participants should note that they are not allowed to post an answer twice....henceforth, double post will attract minus 1 mark

What!!!!
I got the question! All the options are correct. The initial question I opened on my phone had error for option c

smurfy:

What!!!!
I got the question! All the options are correct. The initial question I opened on my phone had error for option c

option I only,option I and II only and option I, II and III are three entirely different choices. When either of the first two options are chosen by a participant, the consequence is that he/she is implying that that option II or III is wrong and the chosen are the only correct options , whichever the case may be

Sent!....choi

Time is Up!!!
Quiz master Doubledx will now post the correct solution
Quiz masters Alphamaximus and Doubledx will send me the names and I will post the new score card

Doubledx na wa 4 ur question o

hope u've received it?

throw question 10 to the floor

Hope it doesn't matter if I send the same answer 2tyms,my mail is doing sumhow

sent! @doubledx, hope u saw my mail...dis question is dem hard...chai...i fear 4 here o...

Alpha Maximus: option I only,option I and II only and option I, II and III are three entirely different choices. When either of the first two options are chosen by a participant, the consequence is that he/she is implying that that option II or III is wrong and the chosen are the only correct options , whichever the case may be

No Maximus. You don't understand. When Richiez first posted the question, the multiple choice I only, II and III only etc. wasn't included. Ask Richiez. Only the answers I, II and III were there. Then option III had a typo. That's why I didn't pick it. I submitted my answer, refreshed the page only to see A, B, C, etc. and correction to option III

denniece1: Doubledx na wa 4 ur question o

d question na war and with limited time

busuyem: throw question 10 to the floor

my chairman, i beg easy o, ur choice of qstns are damn hard,#biko,ogini,please,ejo#....am begging o...easy does things.

Amazing Angel: Hope it doesn't matter if I send the same answer 2tyms,my mail is doing sumhow

if it's same answer, you won't be penalized

D question was not hard,it depend on ♓☺Ϟ•̸ fast Ʊя̲̅ mind thinks

aysuccess99:
my chairman, i beg easy o, ur choice of qstns are damn hard,#biko,ogini,please,ejo#....am begging o...easy does things.

Lolz. U dey fear?

Richiez:
if it's same answer, you won't be penalized

tank God

smurfy:

No Maximus. You don't understand. When Richiez first posted the question, the multiple choice I only, II and III only etc. wasn't included. Ask Richiez. Only the answers I, II and III were there. Then option III had a typo. That's I didn't pick it. I submitted my answer, refreshed the page only to see A, B, C, etc. and correction to option III

when a quiz master posts the solution, it will come with the full question in objectives.
but for this round I will personally remove all objective answers and allow the participants derive the correct answers themselves

mi o she mo, *running out* limited time...busy tinx, O boi, na guessing sure pass. Hope to see some questions that does'nt require more calculation. #Shalom

@Richiez
Please read my comment above and affirm that option c initially had a typo. There was something like and all over the place for option c before the correction. I sent the corrected solution in time. Please adjust the scoreboard for me accordingly. Thanks.

Jst got a better understanding of d question now. ;(

Richiez:

when a quiz master posts the solution, it will come with the full question in objectives.
but for this round I will personally remove all objective answers and allow the participants derive the correct answers themselves

No problem. Please give me my mark. It's such a cheap half-angle formula question.

How many questions are we gonna answer today

@smurfy, I will do so if the quiz masters confirms your statement...hold on

smurfy: @Richiez
Please read my comment above and affirm that option c initially had a typo. There was something like and all over the place for option c before the correction. I sent the corrected solution in time. Please adjust the scoreboard for me accordingly. Thanks.

The typo was sin^(x/2) instead of sin^2(x/2), it was something that was easy to understand... Well, @ richiez I think you should give him the mark!

jaryeh:

How many questions are we gonna answer today

it depends on time....quiz stops by 3:30pm

Option III had the letter b inside square brackets in two places