Exercise
$\csc\left(x\right)^2+\frac{1-\sin^2\left(x\right)}{\sin^4\left(x\right)}=\csc^4\left(x\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Prove the trigonometric identity csc(x)^2+(1-sin(x)^2)/(sin(x)^4)=csc(x)^4. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.
Prove the trigonometric identity csc(x)^2+(1-sin(x)^2)/(sin(x)^4)=csc(x)^4
Final answer to the exercise
true