Question

Sin10° + tan40° × cos10° = ?how to solve this??

Answer 1

You can use the double angle formula

$\sin 2x = 2\sin x \cos x$ and $\cos 2x = 1 - 2\sin^2 x$

and the angle shift identity:

$\cos(90-x) = \sin x\\\sin (90-x) = \cos x$

So:

$\sin 10 + \frac{\sin 40}{\cos 40} \cos 10 = \\\sin 10 + \frac{\sin 40}{\cos 40} \sin 80 =\\ \sin 10 + \frac{\sin 40}{\cos 40} 2 \sin 40 \cos 40 = \\\sin 10 + 2 \sin ^2 40 = \\\cos 80 + \frac{2(1-\cos 80)}{2} = 1$