Exercise
$sec^2x+csc^2x\:\left(tgx+ctgx\right)^2$
Step-by-step Solution
Learn how to solve problems step by step online. Simplify the trigonometric expression sec(x)^2+csc(x)^2(tan(x)+cot(x))^2. Applying the trigonometric identity: \csc\left(\theta \right)^2 = 1+\cot\left(\theta \right)^2. Expand the expression \left(\tan\left(x\right)+\cot\left(x\right)\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Applying the trigonometric identity: \tan\left(\theta \right)\cot\left(\theta \right) = 1. Apply the trigonometric identity: 1+\cot\left(\theta \right)^2=\csc\left(\theta \right)^2.
Simplify the trigonometric expression sec(x)^2+csc(x)^2(tan(x)+cot(x))^2
Final answer to the exercise
$\frac{\sin\left(x\right)^{2}+\csc\left(x\right)^2}{\cos\left(x\right)^2\sin\left(x\right)^{2}}$