Question

If tan α = `1/7`, tan β = `1/3`, then cos 2α = ______.

Options

• sin 2β

• sin 4β

• sin 3β

• None of these

Answer 1

If tan α = `1/7`, tan β = `1/3`, then cos 2α = sin 4β.

Explanation:

Given, tan α = `1/7`, tan β = `1/3`

Now, we have,

cos 2α = `(1 - tan^2 α)/(1 + tan^2 α)`

= `(1 - (1/7)^2)/(1 + (1/7)^2`

= `48/50`

= `24/25`

and cos 2β = `(1 - tan^2 β)/(1 + tan^2 β)`

= `(1 - (1/3)^2)/(1 + (1/3)^2`

= `8/10`

= `4/5`

sin 2β = `(2 tan β)/(1 + tan^2 β)`

= `(2 xx 1/3)/(1 + (1/3)^2`

= `6/10`

= `3/5`

∴ sin 4β = 2 sin 2β cos 2β

= `2 xx 3/5 xx 4/5`

= `24/25`

= cos 2α