Misc 20 - Using the fact that sin (A + B) = sin A cos B - Proofs

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Misc 20 Using the fact that sin ( + )=sin cos +cos sin and the differentiation, obtain the sum formula for cosines. Given sin ( + )=sin cos +cos sin Consider A & B are function of Differentiating both side . . . . sin + = sin cos + cos sin sin + = sin . cos + cos . sin cos + . + = sin . cos + cos . sin cos + . + = sin . cos + cos A + cos . + sin . os A = cos . . cos B sin . sin sin . . sin + cos . . os A = cos . . cos B sin . B sin . . + cos B . . os A = cos cos sin sin + sin sin + cos cos = cos cos sin sin + Thus, cos + . + = cos cos sin sin + cos + . + + = cos cos sin sin cos + = cos cos + sin sin Hence proved

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.