Question

If sin tita+sin square tita=1,then cos12 tita + 3cos10 tita + 3cos8 + cos6 is equal to
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Answer 1

Answer:

1

Step-by-step explanation:

Given,

sinθ + sin²θ = 1

To Find :-

cos¹²θ + 3cos¹⁰θ + 3cos⁸θ + cos⁶θ

Formula Required :-

1) sin²A + cos²A = 1

2) (a + b)³ = a³ + b³ + 3a²b + 3ab²

How To Do :-

As they given a equation we need to simplify it by using a trigonometric identity . Then we will get a value. After that we need to simply given equation by cubing on both sides and we need to substitute the value of equation - 1 in that.

Solution :-

sinθ + sin²θ = 1

sinθ = 1 - sin²θ

sinθ = cos²θ

[ Let it be equation - 1]

sinθ + sin²θ = 1

Cubing on both sides :-

(sinθ + sin²θ)³ = 1³

sin³θ + (sin²θ)³ + 3sinθ(sin²θ)² + 3sin²θ(sin²θ)= 1

sin³θ + sin⁶θ + 3sinθ(sin⁴θ) + 3sin⁴θ= 1

sin³θ + sin⁶θ + 3sin⁵θ + 3sin⁴θ = 1

(sinθ)³ + (sinθ )⁶ + 3 (sinθ )⁵ + 3 (sinθ)⁴ = 1

Substituting the value of equation - 1 :-

(cos²θ )³ + (cos²θ )⁶ + 3 (cos²)⁵ + 3 (cos²θ)⁴ = 1

cos⁶θ  + cos¹²θ  + 3cos¹⁰θ + 3 cos⁸θ  = 1

∴ cos¹²θ + 3cos¹⁰θ + 3cos⁸θ + cos⁶θ = 1