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AP TET Paper 2 Math and Science Model Paper 3

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Question : 107 of 150

Marks: +1, -0

If

tan A + cot A = 2

, then the value of

2(tan^{2} A + cot^{2} A)

is :

1
4
2
3

Solution:

Concept:

Use the identity

\tan A \cdot \cot A = 1

and square the given equation to find

\tan^{2} A + \cot^{2} A

.

Explanation:

Given:

\tan A + \cot A = 2

Square both sides:

(\tan A + \cot A)^{2} = 2^{2}

\tan^{2} A + \cot^{2} A + 2\tan A \cdot \cot A = 4

Since

\tan A \cdot \cot A = 1

, we get:

\tan^{2} A + \cot^{2} A + 2(1) = 4

\tan^{2} A + \cot^{2} A + 2 = 4

\tan^{2} A + \cot^{2} A = 2

Now multiply by 2:

2(\tan^{2} A + \cot^{2} A) = 2 \times 2 = 4

Answer:

The required value is

4

, so the correct option is B.

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