Question

1+cos 7 theta/1+cos theta = (x^3-x^2-2x+1) where x=2 cos theta

Answer 1

Answer:

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Step-by-step explanation:

QUESTION 1. If cotθ=1/√3 then find the value of (1-cos²θ)/(1+cos²θ)

ANSWER : i had used α instead of theta as cot α = 1/√3 & cot 60°=1/√3

⇔cot α=cot 60°

⇔ α=60°

now, there are two methods to solve

1. 1-cos²α/1+cos²α = 1-cos² 60°/1+cos²60°

⇒1-(1/2)²/1+(1/2)²

⇒1-(1/4)/1+(1/4)

⇒4-1/4+1

⇒3/5 Ans

2.1-cos²α/1+cos²α

⇒sin²α/1+cos²α

⇒(√3/2)²/1+(1/2)²

⇒3/4+1

⇒3/5 Ans

QUESTION 2. If tan theta =√3 evaluate (1-cos ^2 theta /1+cos^2 theta)​

ANSWER :

1.       tan θ =√3  

    tan θ = tan 60

      θ  = 60

2.  (1-cos²θ  /1+cos²θ )​

  (1- cos² 60) / 1 +cos² 60)

 (sin ² 60) / 1 +cos² 60)

  ( √3/2 )² / {1 + (1/2)²}

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Answer 2

Answer:

Step-by-step explanation:

As per the question:

Given:

1+cos 7 theta/1+cos theta = (x^3-x^2-2x+1)

To find:

x=2 cos theta

Solution:

α is theta as cot α = 1/√3 & cot 60°=1/√3

cot α=cot 60°

α=60°

now, there are two methods to solve

1. 1-cos²α/1+cos²α = 1-cos² 60°/1+cos²60°

= 1-(1/2)²/1+(1/2)²

= -(1/4)/1+(1/4)

= 4-1/4+1

= 3/5 Ans

2.1-cos²α/1+cos²α

= sin²α/1+cos²α

= (√3/2)²/1+(1/2)²

= 3/4+1

= 3/5 Ans

If tan theta =√3 evaluate (1-cos ^2 theta /1+cos^2 theta)​

1. tan θ =√3  

 tan θ = tan 60

   θ  = 60

2.  (1-cos²θ  /1+cos²θ )​

 (1- cos² 60) / 1 +cos² 60)

(sin ² 60) / 1 +cos² 60)

 ( √3/2 )² / {1 + (1/2)²}

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