Answer:
[tex]\cos ^2\left(x\right)[/tex]
Step-by-step explanation:
You will need to apply some basic trig identities here:
[tex]\sec ^2\left(\frac{\pi }{2}-x\right) \\\\=> \frac{1}{\cos ^2\left(\frac{\pi }{2}-x\right)}\\\\=> \frac{1}{\sin ^2\left(x\right)}[/tex]
Now we substitute this value back into the given equation:
[tex]\left(\frac{1}{\sin \left(x\right)}\right)^2\left(\sin ^2\left(x\right)-\sin ^4\left(x\right)\right)\\\\=> \frac{1\cdot \left(\sin ^2\left(x\right)-\sin ^4\left(x\right)\right)}{\sin ^2\left(x\right)}\\\\=> \frac{\sin ^2\left(x\right)-\sin ^4\left(x\right)}{\sin ^2\left(x\right)}\\\\=> \frac{\sin ^2\left(x\right)\left(1-\sin ^2\left(x\right)\right)}{\sin ^2\left(x\right)}\\\\=> 1-\sin ^2\left(x\right)\\\\=> \cos ^2\left(x\right)[/tex]
Hope that helps!
