Prove

Asked by  | 27th Aug, 2008, 09:01: PM

Expert Answer:

 2cosa cosb cos(a+b) = 2 cosa cosb(cosacosb - sinasinb)

=2cos2a cos2b - 2cosa cosb sina sinb

= cos2a cos2b +cos2a cos2b - 2cosa cosb sina sinb

=(1-sin2a)cos2b + (1-sin2b) cos2a - 2cosa cosb sina sinb

now L.H.S. will be

=cos2a + cos2b -(1-sin2a)cos2b - (1-sin2b) cos2a + 2cosa cosb sina sinb

=sin2a cos2b +sin2b cos2a + 2cosa cosb sina sinb

=(sina cosb+cosa+sinb)2 = sin2(a+b)

Answered by  | 8th Sep, 2008, 06:00: PM

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