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

User Astromax
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1 Answer

2 votes

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\\

User Mercy
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