Question

2. Prove the following identity: sin A+ cos6 A = 1 - 3 sin? A cos? A​

Answer 1

Answer:

L.H.S. =sin

6

θ+cos

6

θ

=(sin

2

θ)

3

+(cos

2

θ)

3

Put sin

2

θ=a and cos

2

θ=b

∴ L.H.S. =a

3

+b

3

=(a+b)

3

−2ab(a+b)

=(sin

2

θ−cos

2

θ)

3

−3sin

2

θcos

2

θ(sin

2

θ+cos

2

θ)

=(1)

3

−3sin

2

θcos

2

θ[∵sin

2

θ+cos

2

θ=1]

=1−3sin

2

θcos

2

θ

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