4cosx cos (pi/3-x) cos (pi/3+x) = cos 3x. prove
Answers
Answered by
94
Step-by-step explanation:
=4cosx*cos(60-x)*cos(60+x)
=4cosx*(cos60*cosx+sin60*sinx)* (cos60*cosx-sin60*sinx)
= 4cosx*(cosx/2 + 3½sinx/2)*(cosx/2 - 3½sinx/2)
= 4cosx*(cos²x/4 - 3sin²x/4)
= 4cosx*(cos²x - 3sin²x)/4
= cosx (cos²x - 3sin²x)
= cosx (cos²x - 3(1-cos²x))
= cosx (cos²x - 3 + 3cos²x)
= cosx (4cos²x - 3)
= 4cos³x - 3cosx
चूँकि ,( cos3x = 4cos³x - 3cosx)
= cos3x (hence proof)
Answered by
32
Answer:
4cosx.cos(60+x).cos(60-x)=cos3x
LHS. 2cosx.[2cos(60+x).cos(60-x)]
=2cosx[cos(60+x+60-x)+cos(60+x-60+x)]
=2cosx[cos 120+cos 2x]
=2cos x[ -1/2 +cos 2x]
=-cos x+2cos 2x.cos x
=-cos x +cos (2x+x) +cos(2x-x)
=-cos x+cos 3x +cos x
=cos 3x proved.
Step-by-step explanation:
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