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AP TET Paper 2 Math and Science Model Paper 3

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Question : 108 of 150

Marks: +1, -0

Simplify: tan (60° - θ) - cot (30° + θ)

$\sqrt 3 + \frac{1}{{\sqrt 3 }}$
$\frac{{2 + \sqrt 3 }}{{\sqrt 3 }}$
0
2√3

Solution:

Concept:

Use the complementary angle identity:

\cot A = \tan(90^\circ - A)

.

Explanation:

Start with the given expression:

\tan(60^\circ - \theta) - \cot(30^\circ + \theta)

.

Rewrite the cotangent term using the identity:

\cot(30^\circ + \theta) = \tan[90^\circ - (30^\circ + \theta)]

.

Simplify the angle:

90^\circ - (30^\circ + \theta) = 60^\circ - \theta

.

So the expression becomes:

\tan(60^\circ - \theta) - \tan(60^\circ - \theta)

.

Subtracting identical terms gives

0

.

Answer:

The value is

0

, so the correct option is C.

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