Verify identity

Question

Verify the identity. Example problem from textbook. 

 

e^sin^2(x) e^tan^2(x) = e^sec^2(x) e^−cos^2(x)

Answer 1

Begin with simplifying the problem by taking the natural log of both sides of the equation.

 

sin²(x) + tan²(x) = sec²(x) - cos²(x)

 

         Use the identity tan²(x) + 1 = sec²(x)

 

sin²(x) + sec²(x) - 1 = sec²(x) - cos²(x)

 

sin²(x) - 1 = -cos²(x)

 

sin²(x) + cos²(x) = 1

 

confirmed