Question

cos2 theta (1+ tan2 theta) +(1+cot 2 theta ) sin2 theta = 2

Answer 1

Answer:

LHS-

cos^2 theta (1+tan^2 theta) + (1+ cot^2 theta) sin^2theta

= cos^2 theta (1+sin^2 theta/cos^2 theta)+(1+cos^2 theta/sin^2 theta) sin^2 theta

= (cos^2 theta ×1 + cos^2 ×sin^2 theta/cos^2 theta )

+ (1× sin^2 theta +cos^2 theta/sin^2 theta ×sin^2 theta)

= (cos^2 theta +sin^2 theta )+(sin^2 theta +cos^2 theta)

= 1+1

= 2

RHS =2

Therefore, LHS = RHS.