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AP TET Paper 2 Math and Science Model Paper 4

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Question : 108 of 150

Marks: +1, -0

If sec A + tan

A = 5

, then sec A - tan A ?

$\frac{2}{5}$
$\frac{5}{2}$
5
$\frac{1}{5}$

Solution:

Concept:

Use the trigonometric identity

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

and factor it as a difference of squares.

Explanation:

Given:

\sec A + \tan A = 5

.

We know:

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

.

Using

a^2 - b^2 = (a - b)(a + b)

, rewrite the identity:

(\sec A - \tan A)(\sec A + \tan A) = 1

.

Substitute the given value of

\sec A + \tan A = 5

:

(\sec A - \tan A) \times 5 = 1

.

Divide both sides by 5:

\sec A - \tan A = \frac{1}{5}

.

Thus, the required value is

\frac{1}{5}

.

Answer:

\sec A - \tan A = \frac{1}{5}

, which is option D.

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