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Question
If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`
Solution
Given that A = 30°
LHS = `(cos^3 "A" – cos 3"A")/(cos "A") + (sin^3 "A" + sin 3"A")/(sin "A")`
= `(cos^3 30° – cos3 (30°))/(cos 30°) + (sin^3 30° + sin3 (30°))/(sin 30°)`
= `((sqrt3/2)^3 – 0)/(sqrt3/2) + ((1/2)^3 + 1)/(1/2)`
= `(sqrt3/2)^2 + (9/8)/(1/2)`
= `(3)/(4) + (9)/(4)`
= `(12)/(4)`
= 3
= RHS
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