Question

1+ sec^2x sin^2x = sec^2x
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation

Answer 1

@surjithayer

Answer 2

\[\begin{align*}1+\sec^2x\sin^2x&=1+\frac{\sin^2x}{\cos^2x}\\
&=1+\tan^2x\\
&=\sec^2x\end{align*}\]
The last step is the Pythagroean identity,
\[\sin^2x+\cos^2x=1~~\iff~~\tan^2x+1=\sec^2x~~\iff~~1+\cot^2x=\csc^2x\]

Answer 3

ok, thank you :)