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Ne4ueva [31]
2 years ago
11

If sin θ = 1/2 , then find the value of (sin 3 θ)/(1+ cos 2 θ)​

Mathematics
1 answer:
Ipatiy [6.2K]2 years ago
7 0

<u>EXPLANATION</u><u>:</u>

Given that

sin θ = 1/2

We know that

sin 3θ = 3 sin θ - 4 sin³ θ

⇛sin 3θ = 3(1/2)-4(1/2)³

⇛sin 3θ = (3/2)-4(1/8)

⇛sin 3θ = (3/2)-(4/8)

⇛sin 3θ = (3/2)-(1/2)

⇛sin 3θ = (3-1)/2

⇛sin 3θ = 2/2

⇛sin 3θ = 1

and

cos 2θ = cos² θ - sin² θ

⇛cos 2θ = 1 - sin² θ - sin² θ

⇛cos 2θ = 1 - 2 sin² θ

Now,

cos 2θ = 1-2(1/2)²

⇛cos 2θ = 1-2(1/4)

⇛cos 2θ = 1-(2/4)

⇛cos 2θ = 1-(1/2)

⇛cos 2θ = (2-1)/2

⇛cos 2θ = 1/2

Now,

The value of sin 3θ /(1+cos 2θ

⇛1/{1+(1/2)}

⇛1/{(2+1)/2}

⇛1/(3/2)

⇛1×(2/3)

⇛(1×2)/3

⇛2/3

<u>Answer</u> : Hence, the req value of sin 3θ /(1+cos 2θ) is 2/3.

<u>also</u><u> read</u><u> similar</u><u> questions</u><u>:</u> If sin Θ = 2/3 and tan Θ < 0, what is the value of cos Θ?

brainly.com/question/12618768?referrer

if cos θ -sin θ =1, find θ cos θ +sin θ?

brainly.com/question/88125?referrer

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