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Prove that: tan5x+tan3x/tan5x-tan3x=4cos2xcos4x Prove that: tan5x+tan3x/tan5x-tan3x=4cos2xcos4x
Hello student,We first consider the L.H.S. and try to reach the R.H.S.L.H.S = = = = (Using the formula sin A cos B + cos A sin B = sin (A+B) ) = = 2 sin 4x cos 4x/sin 2x = 2(2 sin 2x cos 2x)cos 4x/sin 2x = 4 cos 2x cos 4x. = R.H.
== = (Using the formula sin A cos B + cos A sin B = sin (A+B) = 2 sin 4x cos 4x/sin 2x= 2(2 sin 2x cos 2x)cos 4x/sin 2x= 4 cos 2x cos 4x.
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