cos(x)^2+1/csc(x)^2 — step-by-step solution

The cosecant is read as

\csc (u) = \frac{1}{\sin (u)}

, on each interval where

\sin (u) \neq 0

Let's calculate:

{\cos (x)}^{2} + \frac{1}{{(\frac{1}{\sin (x)})}^{2}}

ⓘ The power of a quotient is the quotient of the powers, (a/b)^n = a^n/b^n:

{(\frac{1}{\sin (x)})}^{2}

\frac{1}{{\sin (x)}^{2}}

{\cos (x)}^{2} + \frac{1}{\frac{1}{{\sin (x)}^{2}}}

ⓘ Dividing is multiplying by the reciprocal:

\frac{1}{\frac{1}{{\sin (x)}^{2}}}

{\sin (x)}^{2}

{\cos (x)}^{2} + {\sin (x)}^{2}

ⓘ For every x, cos(x)^2 + sin(x)^2 = 1:

{\cos (x)}^{2} + {\sin (x)}^{2}

1

▶Result:

1