Question

Evaluate: 

`(cos3"A" – 2cos4"A")/(sin3"A" + 2sin4"A")` , when A = 15°

Answer 1

Given that A= 15°

`(cos 3"A"  –  2 cos 4"A")/(sin 3"A" + 2 sin 4"A")`

`= (cos 3 (15°) – 2 cos 4 (15°))/(sin 3 (15°) + 2 sin 4 (15°))`

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

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

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

`= ((1 - sqrt2)/sqrt2)/((1 + sqrt6)/sqrt2)`

= `(1 – sqrt2)/(1+ sqrt6)`