Q. 4

# The value of is

A. cot θ − cosec θ

B. cosec θ + cot θ

C. cosec^{2}θ + cot^{2}θ

D. (cot θ + cosec θ)^{2}

Answer :

__Note: Since all the options involve the trigonometric ratios cosec θ and cot θ, so we divide the whole term (numerator as well as denominator) by sin θ.__

To find:

Consider

Dividing numerator and denominator by sin θ, we get

Rationalizing the term by multiplying it by ,

Now, as 1 + cot^{2} θ = cosec^{2} θ

⇒ cosec^{2} θ – cot^{2} θ = 1

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