Question

Evaluate it

$cot \: = \: \frac{15}{8} \\ \\ \frac{(2 \: + \: 2sin)(1 \: - \: sin)}{(1 + cos)(2 - 2cos)}$<br />

Answer 1

2(1+sin theta)(1-sin theta)/(1-cos theta)(1+cos theta)2

2{1^2 - sin^2 theta}/2{1^2- cos^2theta}

; 1-sin^2 theta / 1- cos^2 theta

; cos^2 theta / sin^2 theta

; cot^2 theta

given cot theta=15/8
there for
cot^2 theta =(15/8)^2=225/64

is your answer

Answer 2

Hi there !

$\frac{(2 + 2sina)(1 - sina)}{(1 + cosa)(2 - 2cosa)} \\ \\ = \frac{2(1 + sina)(1 - sina)}{2(1 + cosa)(1 - cosa)}$

Two will cancel, we get :-


$\frac{1 - {sin}^{2}a }{1 - {cos}^{2}a }$

(Using identity 1-sin2a = cos2A
and 1-cos2a = sin2a )


$\frac{ {cos}^{2} a}{ {sin}^{2}a } = { \cot \: a }^{2}$

In question given that, (15/8)^2 = 225/64

Thanks :)