Question

(1+tan square theta) (1+cot square theta) =1/sin square theta - sin^4 theta​

Answer 1

Answer:

Step-by-step explanation:

wkt (1 + tan^2 theta)  = sec^2 theta

      (1 + cot^2 theta) = cosec^2 theta

      (sec^2 theta)(cosec^2 theta)= 1/(sin^2 theta)(cos^2 theta)

                                           = 1/(sin^2 theta)(1 - sin^2 theta)

                                           = 1/(sin^2 theta - sin^4 theta)

therefore (1+ tan^2 theta)(1+ cot^2 theta)= 1/ (sin^2 theta - sin^4 theta

hence proved

Answer 2

Answer:

Step-by-step explanation:

LHS=(1+tan^2 theta) (1+cot^2theta)

=Sec^2 theta × {cosec^2 theta)

=(1/cos^2 theta × (1/sin^2 theta)

=1/(1-sin^2 theta) × (1/sin^2 theta)

=1/sin^2 theta-sin^4theta