Question

If θ **** in the second quadrant, then show that

√((1-sinθ)/(1+sinθ)) + √((1+sinθ)/(1-sinθ)) = -2secθ

Answer 1

We have

=2/| cos θ| ( Since √α2 = |α| for every real number α)

Given that θ **** in the second quadrant so |cos θ| = – cos θ (since cos θ < 0).

Hence, the required value of the expression is

2/(− cosθ) = –2 secθ