Question

1+sin2a+cos2a /sin2a-cos2a=cotA , pls solve it

Answer 1

Show that cot(A)=(1+sin(2A)+cos(2A))/(1+sin(2A)-cos(2A))

Hi, I have this problem which I don't know how to solve... I know the following identities, but I don't know how to apply them to the problem.

These are the identities I know:

cot(A)=1/tan(A)=sin(A)/cos(A)=sin(2A)/cos(2A)+1

and I also know that sin(2A)=2sin(A)cos(A) and cos(2A)=cos^2(A)-sin^2(A)

Thanks a lot!

Answer 2

$Prove \: that  \: 1+sin2A \: + \: cos \: 2A1 \: + \: sin \: \\ 2A \: − \: cos \: 2A \: \\ = \: cotA</p><p></p><p>Use \:  sin2A \: = \: 2sin \: AcosA \:  and \\ </p><p></p><p>cos2 \: \\ A=1 \: −2sin2A \:  and \:  cos2A \: = \: 2cos2A−1</p><p></p><p>1+sin2A \: + \: cos2A1 \: +sin2A−cos2A=1+2sinAcosA \:+2cos2A−11+2sinAcosA−(1−2sin2A)</p><p></p><p>=2cosA \: (sinA+cosA) \: 2sinA \: (cosA+sinA)</p><p></p><p>=cosAsinA</p><p></p><p>=cotA</p><p></p><p>$

SORRY IF ANY SPACE PROB OCCURS ^^'

AND THANKS FOR THAT thanks In the maths answers ^^""