Prove the following identity: tan(x) + cot(x) = sec(x)csc(x)?

Question

Solve this problem

Answer 1

Given identity : tan(x) + cot (x) = sec(x)csc(x)

Start from Left Hand Side

= tan(x) + cot (x)

Substitute :

Rewrite the expression with common denominator.

Substitute : sin²(x)+cos²(x) = 1

Substitute : 1/ cos(x)  = sec(x)   and   1/sin(x) = csc(x)

= sec(x)csc(x)

Solution :

Trigonometric Identity  tan(x) + cot (x) = sec(x)csc(x) is proved.