Which of the following number (s) is/are rational?
A)sin15°. B)cos15°
C)sin15°cos15°. D) sin15°cos75°

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Solution

Option (C).

Sin 15 cos 15 can be written as

= 1/2 2 sin 15 cos 15 (2 sin a cos a = sin 2a)

= 1/2 sin (2 * 15)

= 1/2 sin 30

= 1/2 * 1/2

= 1/4.

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Similar questions

∣ ∣ ∣ \begin{matrix} cos 15^{\circ} & sin 15^{\circ} sin 75^{\circ} & cos 75^{\circ} \end{matrix} ∣ ∣ ∣

|\begin{matrix} \cos 15 ° & \sin 15 ° \\ \sin 75 ° & \cos 75 ° \end{matrix}|

(cos 75^{\circ} - cos 15^{\circ})^{2} + (sin 75^{\circ} - sin 15^{\circ})^{2}

\frac{\sin 15 ° \cos 75 ° + \cos 15 ° \sin 75 °}{\tan 5 ° \tan 30 ° \tan 35 ° \tan 55 ° \tan 85 °}

Evaluate $∣ ∣ ∣ \begin{matrix} c o s 15 & s i n 15 s i n 75 & c o s 75 \end{matrix} ∣ ∣ ∣$

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