Question

Tan^2a - cot^2a = sec^2a(1-cot^2a) prove

Answer 1

Answer:

sin^2a/cos^2a - cos^2a/sin^a = 1/cos^2a(1-cos^2a/sin^a)

sin^4a-cos^4a/cos^2a*sin^2a = 1/cos^2a - cos^2a/sin^2a*cos^2a

(sin^2a+cos^2a)(sin^2a-cos^2a)/cos^2a*sin^2a = sin^a - cos^2a/cos^2a*sin^2a

(1)(sin^2a-cos^2a)/cos^2a*sin^2a= sin^a - cos^2a/cos^2a*sin^2a

sin^a - cos^2a/cos^2a*sin^2a = sin^a - cos^2a/cos^2a*sin^2a

Hence proved