Question

If sec (theta +a) + sec (theta- a) = 2 sectheta and cos a # 1, then show that cos theta
= = 1/2 cos​

Answer 1

Answer:

sec(θ+α)+sec(θ−α)=2secθ

or

cos(θ+α)

1

+

cos(θ−α)

1

cosθ

2

or

cos(θ+α)cos(θ−α)

cos(θ−α)+cos(θ+α)

=

cosθ

2

or

cos

2

θ−sin

2

α

2cosθcosα

=

cosθ

2

or 2cos

2

θcosα=cos

2

θ−sin

2

α

or sin

2

α=cos

2

θ(1−cosα)

or 1−cos

2

α=cos

2

θ(1−cosα) or 1+cosα=cos

2

θ