If sinA + sin^2A = 1,find the value of cos^12A + 3cos^10A + 3cos^8A + cos ^6A+ 2cos^4A+ 2cos^2 A - 2

Asked by Anjali Sahu | 8th Sep, 2013, 10:30: PM

Expert Answer:

sinA + sin^2A = 1
sinA = 1 - sin^2A = cos^2A
 
Now,  cos^12A + 3cos^10A + 3cos^8A + cos ^6A+ 2cos^4A+ 2cos^2 A - 2  
= (cos^4A)^3 + 3cos^4A cos^2A (cos^4A + cos^2A) + (cos ^2A)^3 + 2(cos^2A)^2 + 2cos^2 A - 2
= (cos^4A + cos^2A)^3 + 2(sinA)^2 + 2 cos^2A - 2
= ((cos^2A)^2 + cos^2A)^3 + 2(sin^2A + cos^2A) - 2
= (sin^2A + cos^2A)^3 + 2(1) - 2
= 1 + 2 - 2 
= 1

Answered by  | 8th Sep, 2013, 10:40: PM

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