Final answer to the problem
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Applying an identity of double-angle cosine: $\cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2$
Learn how to solve trigonometric identities problems step by step online.
$\frac{1}{1-2\sin\left(x\right)^2}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity 1/(1-2sin(x)^2)=sec(2x). Starting from the left-hand side (LHS) of the identity. Applying an identity of double-angle cosine: \cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2. Applying the trigonometric identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Since we have reached the expression of our goal, we have proven the identity.