Question

$sin^{6} \alpha + cos^6 \alpha + 3 \sin^{2} \cos^{2} = 1$
​

Answer 1

Answer:

Prove that :

sin

6

θ+cos

6

θ+3sin

2

θcos

2

θ=1.

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

Step-by-step explanation:

Hope it will help you. Have a great day.