Question

sin theta 1 + sin square theta is equal to cos square theta then prove that cos power 6 theta minus 4 cos power 4 theta + 8 cos square theta is equal to 4​

Answer 1

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EXPLAINATION ➣

Given−

cosθ+cos

2

θ=1

Toprove−

sin

12

θ+3sin

10

θ+3sin

8

θ+sin

6

θ+2sin

4

θ+2sin

2

θ−2=1

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

→cos θ+cos²θ=1

⇒cos θ=1−cos²θ

⇒cos θ= sin²θ

Taking LHS,

⇒(sin⁴θ)3+3 (sin⁴θ)2(sin²θ) +3 (sin⁴θ) (sin²θ)2+(sin²θ)3+2(sin⁴θ+sin²θ)−2(sin⁴θ+sin²θ)3+2(sin⁴θ+sin²θ)−2

➣ Note--- [(a+b)³=a³+b³+3a²b+3ab²]

⇒[(sin²θ)2+sin²θ]3+2[(sin²θ)2+sin²θ]−2

[ sin²θ= cosθ] given

⇒(cos²θ+sin²θ)3+2(cos²θ+sin²θ)−2

[sin²θ+cos²θ = 1]

⇒1³+2−2

⇒1 = 1

LHS=RHS Hence Proved.

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|ʙᴇ ʙʀᴀɪɴʟʏ|

Answer 2

Answer:

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