what is thw solution for prove that :cos6A+6cos4A+15cos2A+10

what is thw solution for
prove that :cos6A+6cos4A+15cos2A+10


1 Answers

19 Points
7 years ago
simply write 6A = 3(2A) and then evaluate it with the aid of cos2A formula. Similarly, write 4A as 2(2A) and evaluate by the same formula. 
finally, you get a cubic in cos2A. take 2A as some x, and make the entire expression, equal to zero.(just for finding A). 
-1 satisfies the equation which looks like this : cos^3(x)(-> cosine cubed x) + 3cos^2(x) + 3cos(x) + 1 = 0. 
cosx = -1. The principal value is just x = pi. Therefore, 2A = pi. A = 90 degrees. 
Substitute this A in the question, and yeah, you get 0. :)

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