Question

value of 15 / cot square theta minus 15 / cos squared theta

Answer 1

-15 is the value of the given question

Answer 2

Answer:

(15/cot²θ) - (15/cos²θ) = -15

Given:

15/cot²θ - 15/cos²θ

Find:

The value of 15/cot²θ - 15/cos²θ.

Solution:

The given expression is,

15/cot²θ - 15/cos²θ = (15/cot²θ) - (15/cos²θ)

But cot θ = cos θ/sin θ

Now, we have

(15/cot²θ) - (15/cos²θ) =  [15/(cos θ/sin θ)²] - [15/cos²θ]

                                   = [15/(cos²θ/sin²θ)] - [15/cos²θ]

                                   = (15 sin²θ/cos²θ) - (15/cos²θ)

                                   =  (15 sin²θ - 15)/cos²θ

                                   =  15(sin²θ - 1)/cos²θ

But sin²θ - 1 = -(1 - sin²θ)

                    = -cos²θ

Putting the value of sin²θ - 1, we get

(15/cot²θ) - (15/cos²θ) = 15(-cos²θ)/cos²θ

                                   = (-15cos²θ)/(cos²θ)

                                   = -15

Hence (15/cot²θ) - (15/cos²θ) = -15

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