Final answer to the problem
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Applying the trigonometric identity: $1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2$
Learn how to solve trigonometric identities problems step by step online.
$\frac{1-\tan\left(x\right)^2}{1+\tan\left(x\right)^2}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (1-tan(x)^2)/(1+tan(x)^2)=1-2sin(x)^2. Starting from the left-hand side (LHS) of the identity. 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)}. Divide fractions \frac{1-\tan\left(x\right)^2}{\frac{1}{\cos\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}.