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AP TET Paper 2 Math and Science Model Paper 1

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Question : 104 of 150

Marks: +1, -0

Find the value of the following expression.

sin(30 + θ) - cos(60 - θ)

$2sin (30 + θ)$
$\frac{\sqrt3}{2}$
0
1

Solution:

Concept:

Use the compound angle formulas for

\sin(A+B)

and

\cos(A-B)

to simplify the expression.

Explanation:

Start with the given expression:

\sin(30^\circ + \theta) - \cos(60^\circ - \theta)

Expand each term using standard identities.

\sin(30^\circ + \theta) = \sin 30^\circ \cos \theta + \cos 30^\circ \sin \theta

\cos(60^\circ - \theta) = \cos 60^\circ \cos \theta + \sin 60^\circ \sin \theta

Substitute the standard values:

\sin 30^\circ = \frac{1}{2}

,

\cos 30^\circ = \frac{\sqrt{3}}{2}

\cos 60^\circ = \frac{1}{2}

,

\sin 60^\circ = \frac{\sqrt{3}}{2}

So the expression becomes:

\left(\frac{1}{2}\cos \theta + \frac{\sqrt{3}}{2}\sin \theta\right) - \left(\frac{1}{2}\cos \theta + \frac{\sqrt{3}}{2}\sin \theta\right)

Simplify by removing brackets:

\frac{1}{2}\cos \theta + \frac{\sqrt{3}}{2}\sin \theta - \frac{1}{2}\cos \theta - \frac{\sqrt{3}}{2}\sin \theta

All terms cancel out.

Therefore, the value is

0

.

Answer:

0

Hence, the correct option is C.

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