Learn how to solve problems step by step online. Prove the trigonometric identity (1+cot(x)^2)/(2cot(x)^2)=(sec(x)^2)/2. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: 1+\cot\left(\theta \right)^2=\csc\left(\theta \right)^2. Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}. Divide fractions \frac{\csc\left(x\right)^2}{\frac{2\cos\left(x\right)^2}{\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}.

Prove the trigonometric identity (1+cot(x)^2)/(2cot(x)^2)=(sec(x)^2)/2