Question

If θ is a positive acute angle such that sec θ = cosec 60°, find 2 cos2 θ – 1

Answer 1

We know that sec (90 – θ) = cosec² θ

Sec θ = sec (90 – 60°)

On equating we get

Sec θ = sec 30°

𝜃 = 30°

To Find 2 cos² θ – 1

`=> 2 xx cos^2 30^@ - 1`    `[cos 30 = sqrt3/2]`

`=>  2 xx (sqrt3/2)^2 - 1`

`=> 2 xx 3/4  - 1`

`=> 3/2 - 1`

`= 1/2`