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Please help in solving this question . If sinA + sin 2 A = 1 . PROVE that cos 12 a +3 cos 10 A + 3 cos 8 A + cos 6 A – 1 = 0 .

Please help in solving this question .
If sinA + sin2A = 1 . PROVE that cos12a +3 cos10A + 3 cos8A + cos6A – 1 = 0 . 

Grade:11

1 Answers

nikesh
39 Points
5 years ago
sinA = 1-sin2A
sinA=cos2A
 
so,
cos12A=sin6A                            …...................(1)
and 3cos8A + 3cos6A=3cos6A(cos2A+cos4A)=3cos2Asin2a(cos2A+sin2A)  …................(2)
                                                                                (as,sinA=cos2A so,sin2A=cos4A)
thus using equations (1) and (2) we have
cos12A+ 3cos10A+3cos8a+cos6A-1
sin6A+3cos2Asin2A(cos2A+sin2A)-1 
 
(sin2A+cos2A)- 1
1-1
0

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