Question

1+cos theta + cosec theta/ 1-cos theta + cosec theta = what

Answer 1

LHS=\frac{cos{\theta}}{cosec{\theta}+1}+\frac{cos{\theta}}{cosec{\theta}-1}

cosecθ+1

cosθ

+

cosecθ−1

cosθ

=\frac{cos{\theta}cosec{\theta}-cos{\theta}+cos{\theta}cosec{\theta}+cos{\theta}}{coec^{2}{\theta}-1}

coec

2

θ−1

cosθcosecθ−cosθ+cosθcosecθ+cosθ

=\frac{cos{\theta}cosec{\theta+cos{\theta}cosec{\theta}}}{cosec^{2}{\theta}-1}

cosec

2

θ−1

cosθcosecθ+cosθcosecθ

=\frac{2cos{\theta}cosec{\theta}}{1-\frac{sin^{2}{\theta}}{sin^{2}{\theta}}}

1−

sin

2

θ

sin

2

θ

2cosθcosecθ

=\frac{2cos{\theta}cosec{\theta}sin^{2}{\theta}}{cos^{2}{\theta}}

cos

2

θ

hope its usefull

2cosθcosecθsin

2

θ

=2tan{\theta}2tanθ

=RHS