Question

Without using tables, evaluate the following: sin60° sin30°+ cos30° cos60°

Answer 1

sin60° sin30°+ cos30° cos60°.

sin60° = `sqrt(3)/(2)`

sin30° = `(1)/(2)`

cos30° = `sqrt(3)/(2)`

cos60° = `(1)/(2)`

sin60° sin30° + cos30° cos60°

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

= `sqrt(3)/(4) + sqrt(3)/(4)`

= `(2sqrt(3))/(4)`

= `sqrt(3)/(2)`.