Question

Prove that. (tan theta + Cot theta + 1)(tan theta + Cot theta - 1)= Sec^2 theta + Cot^2 theta​

Answer 1

Answer:

Hyy dude

Here is your answer:-

First value-

Well, cot theta is reciprocal of tan theta i.e, cot theta = 1/tan theta. If u didn't get it yet let me explain with an example :- suppose cot theta = 1/√3 than tan theta will be reciprocal of this i.e, √3/1 that is √3.

Now,

Proof:- you will understand it better on YouTube with video

Written may not help but still here is your answer:-

To show : \frac{\cot\theta}{1+\tan\theta}=\frac{\cot\theta-1}{2-\sec^2\theta}

Solution :

Taking LHS,

\frac{\cot\theta}{1+\tan\theta}

Rationalize,

=\frac{\cot\theta}{1+\tan\theta}\times\frac{1-\tan\theta}{1-\tan\theta}

=\frac{\cot\theta-\cot\theta\tan\theta}{1^2-\tan^2\theta}

=\frac{\cot\theta-1}{1-(\sec^2\theta-1)}

=\frac{\cot\theta-1}{1-\sec^2\theta+1}

=\frac{\cot\theta-1}{2-\sec^2\theta}

=RHS

So, LHS=RHS