Question

sin^6 10°+cos^6 10°+3 sin²10° cos²10° is​

Answer 1

Step-by-step explanation:

sin6θ+cos6θ+3sin2θcos2θ

⇒LHS=(sin2θ)3+(cos2θ)3+3sin2θcos2θ

Using, [a3+b3=(a+b)3−3ab(a+b)]

⇒LHS=(sin2θ+cos2θ)3−3sin2θcos2θ(sin2θ+cos2θ)3+3sin2θcos2θ

⇒LHS=1−3sin2θcos2θ+3sin2θcos2θ=1=RHS

Answer 2

Answer:

sin

6

θ+cos

6

θ+3sin

2

θcos

2

θ

⇒LHS=(sin

2

θ)

3

+(cos

2

θ)

3

+3sin

2

θcos

2

θ

Using, [a

3

+b

3

=(a+b)

3

−3ab(a+b)]

⇒LHS=(sin

2

θ+cos

2

θ)

3

−3sin

2

θcos

2

θ(sin

2

θ+cos

2

θ)

3

+3sin

2

θcos

2

θ

⇒LHS=1−3sin

2

θcos

2

θ+3sin

2

θcos

2

θ=1=RHS