An algebra problem by Alamuru Ganesh

Algebra Level 3

If c o s θ + cos ⁡ 2 θ = 1 cos \theta + \cos^2 \theta = 1 , Find

sin ⁡ 12 θ + 3 sin ⁡ 10 θ + 3 sin ⁡ 8 θ + sin ⁡ 6 θ + 2 sin ⁡ 4 θ + 2 sin ⁡ 2 θ − 2 \sin^{12} \theta + 3 \sin^{10} \theta + 3 \sin^8 \theta + \sin^6 \theta + 2 \sin^4 \theta + 2 \sin^2\theta - 2


The answer is 1.

Alamuru Ganesh by Alamuru Ganesh , 21, India

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1 solution

cos@= cos^2@ the given becomes sin^6@[sin^6@+3sin^4@+3sin^2@+1]+2[cos^2@+sin^2@]-2 =[cos^3@][cos@+1]^3 =[cos@+cos^2@]^3 = 1^{3} =1

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answer should be -2 or 10 because cos@(1+cos@)=1; => cos@=1or 1+cos@=1=> @=0 or 90=> in putting equation either sin0=0 whatever willbe the power and ans equal to -2 or at @=90 1+3+3+1+2+2-2=10

Shivam Singhal - 6 years, 12 months ago

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