Question

True or false? sec^2*x*tan^2*x*cos^2*x = tan^2*x

Answer 1

Given :

`\sec ^2x\cdot\tan ^2x\cdot\cos ^2x=\tan ^2x`

We need to prove the left side = the right side

so, we should know that:

`\begin{gathered} \cos x=(1)/(\sec x) \\ \cos x\cdot\sec x=1 \end{gathered}`

so,

`\begin{gathered} \sec ^2x\cdot\tan ^2x\cdot\cos ^2x=(\sec ^2x\cdot\cos ^2x)\cdot\tan ^2x \\ =(\sec x\cdot\cos x)^2\cdot\tan ^2x=1^2\cdot\tan ^2x \\ =\tan ^2x \end{gathered}`

so, the left side = the right side

So,

The answer is : True