Question

secθ = m^2+n^2/2mn find the value of √1+sin θ/√1-sin θ

Answer 1

−sinθ1+sinθ−−−−−−−√1−sin⁡θ1+sin⁡θ

=1−sinθ1+sinθ⋅1−sinθ1−sinθ−−−−−−−−−−−−−−−−√=1−sin⁡θ1+sin⁡θ⋅1−sin⁡θ1−sin⁡θ

=(1−sinθ)21−sin2θ−−−−−−−−−−√=(1−sin⁡θ)21−sin2⁡θ

=(1−sinθ)2cos2θ−−−−−−−−−−√=(1−sin⁡θ)2cos2⁡θ

=∣∣∣1−sinθcosθ∣∣∣=|1−sin⁡θcos⁡θ|

=1−sinθ|cosθ|