Question
sin(4x)/sin(x)=4cos(x)cos(x)
verify the identity
verify the identity
Answers
Damon
sin 4 x = 2 sin 2x cos 2x
= 2 (2 sin x cos x)(2cos^2 x - 1)
= 4 sin x (2cos^2 x - 1) cos x
now identity
4 (2cos^2 x - 1) cos x =?4cos^2x
(2cos^2 x -1) = cos x ??
Perhaps I am missing something?
= 2 (2 sin x cos x)(2cos^2 x - 1)
= 4 sin x (2cos^2 x - 1) cos x
now identity
4 (2cos^2 x - 1) cos x =?4cos^2x
(2cos^2 x -1) = cos x ??
Perhaps I am missing something?
MathMate
It is important that the question be copied correctly, whether for posts or for exams.
The question should read:
sin(4x)/sin(x)=4cos(x)cos(2x)
Reduce each side to cos(x) and the identity will be obvious.
The question should read:
sin(4x)/sin(x)=4cos(x)cos(2x)
Reduce each side to cos(x) and the identity will be obvious.