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 + (\sin 40)/(\cos 40) \cos 10 = \\\sin 10 + (\sin 40)/(\cos 40) \sin 80 =\\ \sin 10 + (\sin 40)/(\cos 40) 2 \sin 40 \cos 40 = \\\sin 10 + 2 \sin ^2 40 = \\\cos 80 + (2(1-\cos 80))/(2) = 1\\`