Final Answer
Step-by-step Solution
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Starting from the right-hand side (RHS) of the identity
Multiply $\frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2}$ by $\frac{sin(x)^2+cos(x)^2}{sin(x)^2+cos(x)^2}$
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$\frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sec(x)^2+csc(x)^2=1/(sin(x)^2cos(x)^2). Starting from the right-hand side (RHS) of the identity. Multiply \frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2} by \frac{sin(x)^2+cos(x)^2}{sin(x)^2+cos(x)^2}. Multiplying fractions \frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2} \times \frac{\sin\left(x\right)^2+\cos\left(x\right)^2}{\sin\left(x\right)^2+\cos\left(x\right)^2}. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1.