Question

If sin A = `1/2` and cos B = `1/sqrt2`, then find the value of sin A sin B + cos A cos B.

Answer 1

Given that,

sin A = `1/2` and cos B = `1/sqrt2`

cos A = `sqrt(1 - sin^2 A)`

= `sqrt(1 - (1/2)^2)`

= `sqrt(1 - 1/4)`

= `sqrt(3/4)`

= `sqrt3/2`

sin B = `sqrt(1 - cos^2 B)`

= `sqrt(1 - (1/sqrt2)^2)`

= `sqrt(1 - 1/2)`

= `sqrt(1/2)`

= `1/sqrt2`

⇒ sin A sin B + cos A cos B

⇒ `1/2 xx 1/sqrt2 + sqrt3/2 xx 1/sqrt2`

⇒ `1/(2sqrt2) + sqrt3/(2sqrt2)`

⇒ `(1 + sqrt3)/(2sqrt2)`