Question

If sec A = `sqrt(2)` and tan B = `sqrt(3)`, then find the value of 2 sin A cos B.

Answer 1

Given:

`sec A = sqrt(2)`

`tan B = sqrt(3)`

Finding angles A and B:

`sec A = sqrt(2)` ⇒ A = 45°

`tan B = sqrt(3)` ⇒ B = 60°

Finding values of sin A and cos B:

`sin A = sin 45^circ = 1/sqrt(2)`

`cos B = cos 60^circ = 1/2`

Calculating the required value:

`2 sin A cos B = 2 xx 1/sqrt(2) xx 1/2`

= `1/sqrt(2)`

= `sqrt(2)/2`