# $\cos^2 70^\circ + \cos 25^\circ.\sin 25^\circ$ [closed]

Find the value of :- $\cos^2 70^\circ + \cos 25^\circ.\sin 25^\circ$ without using trigonometric table . Formulas may be used :-

$\cos (180-A ) = -\cos A$

$\sin ( 180-A ) = \sin A$

$\sin 2A = 2 \sin A .\cos A$

$\cos 2A = 1-2\sin^2A$

## closed as off-topic by Jack D'Aurizio, Carl Mummert, Michael Albanese, 6005, Zain PatelJul 24 '16 at 21:48

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## 1 Answer

$$\cos 2\theta=2\cos^2\theta -1$$ $$\implies \cos^2 70 =\frac{cos140^{\circ} +1}{2}$$ $$cos140^{\circ}=-cos50^{\circ}$$ $$\cos 25^\circ.\sin 25^\circ=\frac{\sin 50^\circ}{2}$$