Question

Evaluate the following:

sin 45° sin 30° + cos 45° cos 30°

Answer 1

sin 45° sin 30° + cos 45° cos 30° …...(i)

We know that by trigonometric ratios we have,

`sin 45^@ = 1/sqrt2 sin 30^@ = 1/2`

`cos 45^@ = 1/sqrt2 cos 30^@ = sqrt3/2`

Substituting the values in (i) we get

`1/sqrt2 . 1/2 + 1/sqrt2 . sqrt3/2`

`= 1/sqrt2 . sqrt3/(2sqrt2) = (sqrt3 + 1)/(2sqrt2)`