If cosec²θ = 100/71, then what is the value of cot²θ?

Correct Answer is : 297129/717129

Correct Answer is : 297129/717129

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AP TET Paper 2 Math and Science Model Paper 1

Question : 103 of 150

Marks: +1, -0

cosec^{2}θ = \frac{100}{71}

cot^{2}θ

Solution:

Concept:

Use the trigonometric identity

\csc^{2}\theta = 1 + \cot^{2}\theta

Explanation:

Given

\csc^{2}\theta = \frac{100}{71}

Substitute into the identity:

\frac{100}{71} = 1 + \cot^{2}\theta

Rearrange to isolate

\cot^{2}\theta

\cot^{2}\theta = \frac{100}{71} - 1

Write

1

\frac{71}{71}

\cot^{2}\theta = \frac{100}{71} - \frac{71}{71}

Subtract the fractions:

\cot^{2}\theta = \frac{29}{71}

Answer:

\cot^{2}\theta = \frac{29}{71}

, which is option A.

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