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If sin Î± + sin Î² = a and cos Î± + cos Î² = b,then prove that sin(Î± + Î²) = (2ab/a² + b²)

#Mathematics #Trignometry #Trigonometric functions

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Sushovan Halder ·2014-07-17 05:49:04

put the values of a and b to get the answer

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ARKADYUTI BANDYOPADHYAY I have tried. It does not work.
Upvote·0· Reply ·2014-07-17 06:08:18
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Amartya Kumar Mistry ·2014-07-22 03:14:35

the best method is by using transformation of sums and products
by using that a=2sin(Î±+Î²)/2 *cos(Î±-Î²)/2-(1) and for b=2cos(Î±+Î²)/2 *cos(Î±-Î²)/2-(2)
now dividing (1) by (2) we get tan(Î±+Î²)/2=a/b
now simply using the formula of sin2Î¸=2tanÎ¸/1+tan^2Î¸ the identity will be proved

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