Question

Prove that : 2 (sin6 0 + cos6 0) – 3 (sin4 0 + cos4 0) + 1 = 0.​

Answer 1

Step-by-step explanation:

2{(sin60+cos(90-30)} - 3 {(sin40 + cos(90-50)} +1 =0

2{sin(60) + cos 30} - 3 {sin 40 + sin 50} + 1

now out values of sin60 and cos 30 and apply formula of sin A + sin B , so you will get your answer

Answer 2

Answer:

LHS=2(sin

6

θ+cos

6

θ)−3(sin

4

θ+cos

4

θ)+1

=2{(sin

2

θ+cos

2

θ)

3

−3sin

2

θcos

2

θ(sin

2

θ+cos

2

θ)}−3(sin

2

θ+cos

2

θ)

2

−2(sin

2

θcos

2

θ)}+1

We know, [sin²x+cos²x=1]

=2{1−3sin

2

θcos

2

θ}−3{1−2sin

2

θcos

2

θ}+1

=2−6sin

2

θcos

2

θ−3+6sin

2

θcos

2

θ+1

=0

=RHS