Numerical value of cos- 12 sin 5- 12 -cos- 4 -sin- 12 cos 5- 12 -sin- 4

The correct option is B 3 2 =(cosπ12sin5π12+sinπ12cos5π12)+(cosπ12cosπ4 sinπ12sinπ4)=sin(π12+5π12)+cos(π12+π4) =sinπ2+cosπ3=1+12=32 Therefore, An ...

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Principal Solution of Trigonometric Equation

Numerical val...

Question

Numerical value of $cos \frac{π}{12} (sin \frac{5 π}{12} + cos \frac{π}{4}) + sin \frac{π}{12} (cos \frac{5 π}{12} - sin \frac{π}{4})$

\frac{1}{2}

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\frac{3}{2}

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2 + \sqrt{3}

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

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cos \frac{π}{12} (sin \frac{5 π}{12} + cos \frac{π}{4}) + sin \frac{π}{12} (cos \frac{5 π}{12} - sin \frac{π}{4})

cos \frac{π}{4} \times (cos \frac{π}{12} - sin \frac{π}{12})

cos \frac{π}{12} - sin \frac{π}{12} = \frac{1}{\sqrt{2}}

{⎛ ⎜ ⎜ ⎜ ⎝ \frac{cos (\frac{π}{2} + x) + sin (\frac{π}{2} + x)}{cos (\frac{π}{2} - x) - sin (\frac{π}{2} - x)} ⎞ ⎟ ⎟ ⎟ ⎠}^{2}

Q = ⎡ ⎢ ⎢ ⎣ \begin{matrix} cos \frac{π}{4} & - sin \frac{π}{4} sin \frac{π}{4} & cos \frac{π}{4} \end{matrix} ⎤ ⎥ ⎥ ⎦

x = ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦

Q^{3} x

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