Simplify {1}{(sin²A)}-1 where 0

Correct Answer is : cot2Acot² Acot2A

Correct Answer is : cot2Acot² Acot2A

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RRB Technician Grade I 20 Dec 2024 Shift 1 Paper

Question : 87 of 100

Marks: +1, -0

Simplify

\frac{1}{(sin^{2}A)}-1

where 0 < A ≤ 90º

Solution:

Concept:

Use the Pythagorean identity

\csc^2 A - 1 = \cot^2 A

Explanation:

Given expression:

\frac{1}{\sin^2 A} - 1

Since

\frac{1}{\sin A} = \csc A

, we have

\frac{1}{\sin^2 A} = \csc^2 A

So the expression becomes

\csc^2 A - 1

Using the identity

\csc^2 A - 1 = \cot^2 A

, we get the simplified form.

Thus,

\frac{1}{\sin^2 A} - 1 = \cot^2 A

Answer:

\cot^2 A

(Option A).

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