O-Level Additional Math

[heutistmeintag]

Need help on Sec 3 A maths Trigo question:

Given that cosec A + cot A = 3, evaluate cosec A - cot A and cos A.

Thanks in advance!

[FrekiWang]

heutistmeintag:

Need help on Sec 3 A maths Trigo question:

Given that cosec A + cot A = 3, evaluate cosec A - cot A and cos A.

Thanks in advance!

Sorry I feel lazy to solve it in a standard approach.
1/sinA + cosA/sinA = 3
1 + cosA = 3sinA ...(1)
Let cosecA - cotA = k
1/sinA - cosA/sinA = k
1 - cosA = ksinA ...(2)
(1)*(2) we have,
1 - (cosA)^2 = 3k(sinA)^2
(sinA)^2 = 3k(sinA)^2
3k = 1
k = 1/3 (this is the value of cosecA - cotA)

subst k = 1/3 into (2), we have
1 - cosA = 1/3sinA ... (3)
(1) - (3)*9, we have
(1+cosA) - 9(1-cosA) = 0
-8 + 10cosA = 0
cosA = 0.8

[red rose]

Need help to solve this.


x - 2/x + 3 = 2x^2 + x - 10/x^2 + 6x + 9

I only managed to get x = -2, but the answer key says the answer should be x = 2 or x = -2. Please advise.

Thank you in advance.

[jtoh]

Hi red rose,


I'm a little confused with the presentation of the question - limitations of typing out the question. Could you please clarify if it's :

x - 2/x + 3 or (x-2)/(x+3)

Similarly for the right hand side? Thanks.

[red rose]

jtoh:

Hi red rose,


I'm a little confused with the presentation of the question - limitations of typing out the question. Could you please clarify if it's :

x - 2/x + 3 or (x-2)/(x+3)

Similarly for the right hand side? Thanks.

Hi! It's with brackets. Eg. (x-2) divided by (x+3)

Thanks!

[jtoh]

Thanks red rose. So the right hand side is (2x^2 + x - 10)/(x^2 + 6x + 9)?

[red rose]

jtoh:

Thanks red rose. So the right hand side is (2x^2 + x - 10)/(x^2 + 6x + 9)?

Yes! :thankyou:

[jtoh]

Hi red rose, I only managed to get x = -2 too. Could the answer sheet be wrong? Is this question from a workbook?

[red rose]

jtoh:

Hi red rose, I only managed to get x = -2 too. Could the answer sheet be wrong? Is this question from a workbook?

Nope. It's from a Sec 2 IP school revision worksheet. Thanks for trying anyway. The curious thing is, +2 works too when substituted into the equation.

[jtoh]

red rose:

jtoh:

Hi red rose, I only managed to get x = -2 too. Could the answer sheet be wrong? Is this question from a workbook?

Nope. It's from a Sec 2 IP school revision worksheet. Thanks for trying anyway. The curious thing is, +2 works too when substituted into the equation.

Hmm... are we approaching the question wrongly from our archaic math training? Could your dd get the answer? I'll ask my dd to try it later. Is this the school's worksheet?