Question

Sin(pi/2-x)/cot^2(pi/2-x)+1

Answer 1

Answer:

${ \cos}^{3} x$

Step-by-step explanation:

We want to simplify:

$\frac{ \sin( \frac{\pi}{2} - x) }{ { \cot}^{2} ( \frac{\pi}{2} -1 ) + 1}$

Use the Pythagorean identity:

${ \csc}^{2}x = { \cot}^{2}x + 1$

We apply this property to get:

$\frac{ \sin( \frac{\pi}{2} - x) }{ { \csc}^{2} ( \frac{\pi}{2} -x) }$

This gives us:

$\frac{ \sin( \frac{\pi}{2} - x) }{ \frac{1}{{ \sin}^{2} ( \frac{\pi}{2} -x)} }$

We simplify to get:

$\sin^{3} ( \frac{\pi}{2} -x)$

$(\sin ( \frac{\pi}{2} -x))^{3}$

Apply the complementary identity;

$(\cos x)^{3} = { \cos}^{3} x$