Final answer to the problem
Step-by-step Solution
Specify the solving method
Apply the trigonometric identity: $\csc\left(\theta \right)^n$$=\frac{1}{\sin\left(\theta \right)^n}$, where $n=2$
Learn how to solve simplify trigonometric expressions problems step by step online.
$\frac{1+\tan\left(x\right)^2}{\frac{1}{\sin\left(x\right)^2}}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (1+tan(x)^2)/(csc(x)^2). Apply the trigonometric identity: \csc\left(\theta \right)^n=\frac{1}{\sin\left(\theta \right)^n}, where n=2. Divide fractions \frac{1+\tan\left(x\right)^2}{\frac{1}{\sin\left(x\right)^2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Applying the trigonometric identity: 1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.