Question

Hello, can you please help me solve question five !

Answer 1

5. To verify:

`(1)/(\cos x\csc^2x)=\sec x-\cos x`

Considering the left hand side,

`\begin{gathered} (1)/(\cos x\csc^2x)=(1)/(\cos x)\cdot\sin ^2x\text{ (since, }(1)/(csc^2x)=\sin ^2x) \\ =(1)/(\cos x)(1-\cos ^2x)\text{ (since},\text{ sin}^2x=1-\cos ^2x) \\ =(1)/(\cos x)-\cos x \\ =\sec x-\cos x \end{gathered}`

Hence verified.