Question

Prove that 2(sin⁶0+ cos⁶0)-3(sin⁴ 0+ cos⁴0) is equal to-1.​

Answer 1

Answer:

Step-by-step explanation:

To Prove :-

2(sin⁶0+ cos⁶0)-3(sin⁴ 0+ cos⁴0) = - 1

Solution :-

Taking L.H.S :-

$= 2(sin^6\theta+cos^6\theta)-3(sin^4\theta+cos^4\theta)$

$= 2((sin^2\theta)^3+(cos^2\theta)^3)-3((sin^2\theta)^2+(cos^2\theta)^2)$

$=2((sin^2\theta+cos^2\theta)^3-3sin^2\theta cos^2\theta(sin^2\theta+cos^2\theta))-3((sin^2\theta+cos^2\theta)^2-2sin^2\theta cos^2\theta)$

$=2((1)^3-3sin^2\theta cos^2\theta(1))-3((1)^2-2sin^2\theta cos^2\theta)$

$=2(1-3sin^2\theta cos^2\theta)-3(1-2sin^2\theta cos^2\theta)$

$= 2 - 6sin^2\theta cos^2\theta-3+6sin^2\theta cos^2\theta$

$= 2 - 3$

= - 1

= R.H.S

Hence Proved.

Know More :-

Trigonometric Identities :-

$1) sin^2\theta+cos^2\theta=1$

$2)sec^2\theta-tan^2\theta=1$

$3)csc^2\theta-cot^2\theta=1$