Question

prove that (1-cos²theta)(1+tan²theta)=tan²theta ​

Answer 1

Let theta=x

${\underline{ \mathtt{\red{tan^4x+} \green{tan^2x=}\mathtt\blue{sec^4x} \purple{} \mathtt \orange{-sec^2x}\pink{}}}}\:$

L.H.S.

${\underline{ \mathtt{\red{} \green{}\mathtt\blue{=tan^2x.(tan^2 x +1)} \purple{} \mathtt \orange{}\pink{}}}}\:$

${\underline{ \mathtt{\red{} \green{On-putting}\mathtt\blue{} \purple{} \mathtt \orange{}\pink{}}}}\:$ ${\underline{ \mathtt{\red{} \green{}\mathtt\blue{} \purple{tan ^2 x=sec^2x-1} \mathtt \orange{}\pink{}}}}\:$

${\underline{ \mathtt{\red{} \green{}\mathtt\blue{} \purple{=(sec^2x-1).(sec^2x-1+1)} \mathtt \orange{}\pink{}}}}\:$${\underline{ \mathtt{\red{} \green{}\mathtt\blue{} \purple{} \mathtt \orange{=(sec^2x-1).(sec^2x-1+1)}\pink{}}}}\:$

${\underline{ \mathtt{\red{} \green{}\mathtt\blue{} \purple{=(sec^2 x- 1).sec^2 x} \mathtt \orange{}\pink{}}}}\:$

${\underline{ \mathtt{\red{} \green{}\mathtt\blue{} \purple{} \mathtt \orange{}\pink{= sec^4 x - sec^2x}}}}\:$. ${\underline{ \mathtt{\red{} \green{Proved}\mathtt\blue{} \purple{} \mathtt \orange{}\pink{}}}}\:$.

Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘs

Answer 2

Answer:

I hope it's help you✌︎✌︎...