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Telangana TET Paper 2 Math and Science Model Paper 5

Section: Math and Science

Question : 95 of 150

Marks: +1, -0

\rm \frac{1}{cosec^2 θ - cot^2 θ} + \frac{1}{sec^2 θ - tan^2 θ}= 2 \ sin\ θ

, then one of the value of θ is:

Solution:

Concept:

Use trigonometric identities to simplify denominators:

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

and

\sec^2\theta - \tan^2\theta = 1

Explanation:

Rewrite the given equation using the identities:

\frac{1}{1} + \frac{1}{1} = 2\sin\theta

2 = 2\sin\theta

Divide both sides by 2:

1 = \sin\theta

We know

\sin\theta = 1

when

\theta = 90^\circ

Answer:

\theta = 90^\circ

(Option D)

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