Find the value of $cos 15^{\circ}$

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

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

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

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

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Solution

The correct option is B $\frac{\sqrt{3} + 1}{2 \sqrt{2}}$
We know that $cos (a - b) = cos a cos b + sin a sin b$

So, $= cos 15 = cos (45 - 30) = cos 45 cos 30 + sin 45 sin 30 = \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}} \times \frac{1}{2} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

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Similar questions

\frac{1}{1 + \frac{1}{3 - \frac{4}{2 + \frac{1}{3 - (\frac{1}{2})}}}} + \frac{3}{3 - \frac{4}{3 + \frac{1}{2 - (\frac{1}{2})}}}

Find the value of:

$(1) (2^{0} + 3^{- 1}) \times 3^{2}$

$(i i) (2^{- 1} \times 3^{- 1}) \div 2^{- 3}$

$(i i i) {(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2}$

c o s 15^{\circ} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}

c o s (A - B) = c o s A c o s B + s i n A s i n B

{{(\frac{1}{3})}^{- 2} - {(\frac{1}{2})}^{- 3}} \div {(\frac{1}{4})}^{- 2}

1 + \frac{1}{1 + 2} + \frac{1}{1 + 2 + 3} + . . . . . . . . . . . + \frac{1}{1 + 2 + 3 + 4... n}

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