1. ## Prove this idenity

Thanks

2. Originally Posted by smmmc
Thanks
Just substitute $\tfrac{\sin\theta}{\cos\theta}$ for $\tan\theta$ and $\tfrac{\cos\theta}{\sin\theta}$ for $\cot\theta$. After cancelling the denominators on the left side of the equation you get $\sin^2\theta+\cos^2\theta=1$, which is surely true for all $\theta$.

3. so it becomes

cos^2theta * sintheta/costheta + sin^2theta * cos theta/sin theta

= cos theta*sin theta + sin theta*cos theta

how does this equal to 1 ?

You forgot that the question is $\tan^2\theta$ and $\cot^2\theta$, not $\tan\theta$ and $\cot\theta$
5. $cos^2(x)*tan^2(x)+sin^2(x)*cot^2(x)$
$=cos^2(x)\frac{sin^2(x)}{cos^2(x)}+sin^2(x)\frac{c os^2(x)}{sin^2(x)}$
$=sin^2(x)+cos^2(x)=1$