SOLUTION: 1) [(sin3x)/(sinx)] - [(cos3x)/ (cosx)]= 2

Algebra ->  Trigonometry-basics -> SOLUTION: 1) [(sin3x)/(sinx)] - [(cos3x)/ (cosx)]= 2       Log On


   

Question 442985: 1) [(sin3x)/(sinx)] - [(cos3x)/ (cosx)]= 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
To prove this, we manipulate the left-hand side (LHS) of the given equation to reach the right-hand side. That is:
=+sin%283x%29+%2F+sin%28x%29+-+cos%283x%29+%2F+cos+%28x%29

= %28+sin%283x%29+cos%28x%29+-+cos%283x%29+sin+%28x%29+%29+%2F+%28+sin%28x%29+cos%28x%29+%29.

=sin%283x+-+x%29+%2F+%28+sin%28x%29+cos%28x%29+%29 by applying difference of two angles identity for sine function

=sin%282x%29+%2F+%28+sin%28x%29+cos%28x%29%29 by simplification

= %282+sin%28x%29+cos%28x%29+%29+%2F%28+sin%28x%29+cos%28x%29+%29 by double-angle identity for sine function

= 2+%28sin%28x%29+cos%28x%29+%29+%2F+%28+sin%28x%29+cos%28x%29+%29 by factoring

= 2+%2Across%28%28sin%28x%29+cos%28x%29+%29%29+%2F+cross%28%28+sin%28x%29+cos%28x%29%29+%29
= 2