Question

If x and y are acute angles, such that cos x + cos y = `3/2` and sin x + sin y = `3/4`, then sin (x + y) equals:

पर्याय

• `2/5`

• `3/4`

• `3/5`

• `4/5`

Answer 1

`bb(4/5)`

Explanation:

Given, cos x + cos y = `3/2`

`\implies 2 cos ((x + y)/2) cos((x - y)/2) = 3/2`  ...(i)

and sin x + sin y = `3/4`

`\implies 2 sin((x + y)/2) cos((x - y)/2) = 3/4`  ...(ii)

On dividing equation (i) by equation (ii), we get

`(2 sin((x + y)/2) cos((x - y)/2))/(2 cos((x + y)/2) cos((x - y)/2)) = (3/4)/(3/2)`

`\implies tan((x + y)/2) = 1/2`

∴ sin (x + y) = `(2 tan ((x + y)/2))/(1 + tan^2 ((x + y)/2))`

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

= `4/(4 + 1)`

= `4/5`