Explanation: 1. Identify the values: 2. Substitute the values into the equation: 3. Simplify the terms: 4. Combine the fractions (Common Denominator):

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NIMCET 2011 Mathematics PYQ — The value of is:… | Mathem Solvex

A.
$\frac{1-\sqrt{3}}{2}$
B.
$\frac{1+\sqrt{3}}{2\sqrt{2}}$

Correct Answer:

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

Explanation

1. Identify the values:

$\sin 30^\circ = \frac{1}{2}$
$\cos 45^\circ = \frac{1}{\sqrt{2}}$
$\cos 30^\circ = \frac{\sqrt{3}}{2}$
$\sin 45^\circ = \frac{1}{\sqrt{2}}$

2. Substitute the values into the equation:

\sin 30^\circ \cos 45^\circ + \cos 30^\circ \sin 45^\circ

\left( \frac{1}{2} \times \frac{1}{\sqrt{2}} \right) + \left( \frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{2}} \right)

3. Simplify the terms:

\frac{1}{2\sqrt{2}} + \frac{\sqrt{3}}{2\sqrt{2}}

4. Combine the fractions (Common Denominator):

\frac{1 + \sqrt{3}}{2\sqrt{2}}

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NIMCET 2011 — Mathematics PYQ

Choose the correct answer:

Explanation

Explanation