(Cos cube alpha - cos 3 alpha)/ cos alpha + ( sin cube alpha + sin 3 alpha) / sin - Maths - Trigonometric Functions

Question

(Cos cube alpha - cos 3 alpha)/ cos alpha + ( sin cube alpha + sin
3 alpha) / sin alpha = 3

Varun.Rawat · Accepted Answer

LHS = cos3α - cos 3αcos α + sin3α + sin 3αsin α=cos3α - 4 cos3α - 3 cos αcos α + sin3α + 3 sin α - 4 sin3αsin α=3 cos α - 3 cos3αcos α + 3 sin α - 3 sin3αsin α=3 - 3 cos2α + 3  - 3 sin2α=6 - 3sin2α + cos2α=6 - 3=3=RHS

(Cos cube alpha - cos 3 alpha)/ cos alpha + ( sin cube alpha + sin 3 alpha) / sin alpha = 3