Question

The x in the problem is actually theta...so...
show that 1+cot^2x - cos^2x-cos^2xcot2x=1

Answer 1

\[1+\cot^2x-\cos^2x-\cos^2x \cot(2x)=1?\]

Answer 2

oh i meant 1+cot^2x−cos^2x−cos^2xcot^2x=1?

Answer 3

\[\begin{align*}1+\cot^2x-\cos^2x-\cos^2x\cot^2x&=1\\
1-\cos^2x+\cot^2x-\cos^2x\cot^2x&=\\
1-\cos^2x+\cot^2x\left(1-\cos^2x\right)&=\\
\left(1+\cot^2x\right)\left(1-\cos^2x\right)&=
\end{align*}\]
Any identities you can think of?

Answer 4

the last one switch it to csc^2x(sin^2x) ?

Answer 5

maybe like this :
let's do from left side :
1+cot^2x - cos^2x - cos^2xcot2x
= 1+cot^2x - (cos^2 x)(1+cot^2x)
= (1+cot^2x)(1 - cos^2 x)
= (1+cot^2x)sin^2 x
= csc^2 x sin^2 x
= 1/sin^2 x * sin^2 x
= 1

Answer 6

@kungfupichu, yes, that's it. Now what can you rewrite that as?

Answer 7

Actually, @RadEn already showed what you can do.