Question

prove that:
√sec O - 1/ sec O + 1 + √sec O + 1/ sec O - 1 = 2 cosec O​

Answer 1

Step-by-step explanation:

secθ−1secθ+1−−−−−−−√+secθ+1secθ−1−−−−−−−√

=1cosθ−11cosθ+1−−−−−−−⎷+1cosθ+11cosθ−1−−−−−−−⎷

=1−cosθ1+cosθ−−−−−−−√+1+cosθ1−cosθ−−−−−−−√

=2sin2θ22cos2θ2−−−−−−−⎷+2cos2θ22sin2θ2−−−−−−−⎷

=tanθ2+cotθ2

=tanθ2+1tanθ2

=tan2θ2+1tanθ2

=sec2θ2tanθ2

=1cos2θ2sinθ2cosθ2

=1cosθ2sinθ2

=2sinθ

=2Cosecθ