Question

Evaluate : 

`(3 sin 3"B" + 2 cos(2"B" + 5°))/(2 cos 3"B" – sin (2"B" – 10°)` ; when "B" = 20°.

Answer 1

Given that B = 20°

`(3 sin 3"B"+2 cos(2"B"+5°))/(2 cos 3"B" – sin (2"B" – 10°)` = `(3 sin 3 xx 20°+2 cos(2 xx 20°+5°))/(2 cos 3 xx 20° – sin (2 xx 20° – 10°))`

= `( 3 sin 60° + 2 cos 45°)/(2 cos 60° – sin 30°)`

= `(3(sqrt3/2) + 2(1/sqrt2))/(2(1/2) – (1)/(2)`

= `(3(sqrt3)/(2) + sqrt2)/(2)`

= `3 sqrt3  + 2 sqrt2`