Question

if cosec theta + cot theta is equal to P then prove that cos theta is equal to p square minus one upon p square + 1 ​

Answer 1

hope this helps you.....

Answer 2

Answer:

Step-by-step explanation:

Question: if cosec θ + cot θ  is equal to P then prove that cos θ  is equal to p² -1 upon p² + 1 ​.

To Prove: The value of cosθ =p² -1 /p² + 1 ​.

Given: cosec cosec θ + cot θ = P  + cot θ = P

Explanation:-

Now According to the Question:-

cosec θ + cot θ = P -----(1)

We know that,

Cosec²  θ - Cot² θ= 1

=( cosec θ + cot θ )(cosec θ - cot θ )=1

= (cosec θ - cot θ )P =1

= (cosec θ - cot θ ) = 1/P -----(2)

Adding (1) and (2) :-

2Cosec θ = P+1/P

                  = (P²+1)/P

Cosecθ = C/2P

Sinθ  = 2P/ (P²+1)

Cosθ = √1-sin²θ

        =√1-4P²/(P²+1)

      = P²-1/P²+1

Hence proved

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