Question

Without using tables, evaluate the following: sin²30° sin²45° + sin²60° sin²90°.

Answer 1

sin²30° sin²45° + sin²60° sin²90°

sin30° = `(1)/(2)`

sin45° = `(1)/sqrt(2)`

sin60° = `sqrt(3)/(2)`

sin90° = 1
sin²30° sin²45° + sin²60° sin²90°

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

= `(1)/(4) xx (1)/(2) + (3)/(4)`

= `(1)/(8) + (3)/(4)`

= `(1 + 6)/(8)`

= `(7)/(8)`.