Math, asked by aryasatagopal, 1 month ago

cos6 A + sin6 A = 1 - 3sin2 A . cos2A​

Answers

Answered by amansharma264
4

EXPLANATION.

⇒ cos⁶(A) + sin⁶(A) = 1 - 3sin²A.cos²A.

As we know that,

We can write equation as,

⇒ [(cos²A)³ + (Sin²A)³].

As we know that,

Formula of :

⇒ a³ + b³ = (a + b)³ - 3ab(a + b).

Using this formula in equation, we get.

⇒ [cos²A + sin²A]³ - 3cos²A.sin²A(cos²A + sin²A).

As we know that,

Formula of :

⇒ sin²x + cos²x = 1.

Using this formula in equation, we get.

⇒ 1 - 3cos²A.sin²A.

Hence proved.

                                                                                                                       

MORE INFORMATION.

Trigonometrical ratios of multiple angles.

(1) = sin2θ = 2sinθcosθ = 2tanθ/1 + tan²θ.

(2) = cos2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ = 1 - tan²θ/1 + tan²θ.

(3) = tan2θ = 2tanθ/1 - tan²θ.

(4) = sin3θ = 3sinθ - 4sin³θ.

(5) = cos3θ = 4cos³θ - 3cosθ.

(6) = tan3θ = 3tanθ - tan³θ/1 - 3tan²θ.

Answered by Itsgoodnation
0

Answer:

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