Question

if cos theta =4/5, show that cot2 theta -cos2 theta=cot2 theta ×cos2 theta​

Answer 1

Given: cos = 4/5

TST: cot^2 - cos^2 = (cot^2)(cos^2)

LHS= cot^2 - cos^2

= 1/tan^2 - 1/sec^2

= sec^2 - tan^2/(sec^2)(tan^2)

= 1 + tan^2 - tan^2/ (1/cos^2) (sin^2/cos^2)

= (cos^2) (cos^2/sin^2)

= (cos^2) (cot^2) = RHS

Thus LHS=RHS.

{sec^2=1 + tan^2

sec^2=1/cos^2

tan^2=1/cot^2=sin^2/cos^2}