Question

when is an equation called an identity .prove that 1+tan²A=sec²A

Answer 1

By Pythagorean Theorem,

Hence ,

           sin2x + cos2x = 1

Proof  : tan²A + 1 = sec²A

From ,sin²A + cos²A = 1

sin²A/cos²A + cos²A/cos²A = 1/cos²A

(sin A/cos A)² + 1 = (1/cos A)²

tan²A + 1 = sec²A

hence proved

Proof f: 1 + cot2x = csc2x

sin²A/sin²A + cos²A/sin²A = 1/sin²A

by squared on both sides,

(cos A/sin A)² + 1 = (1/sin A)²

1 + cot2x = csc2x