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