cos-2-70-sin-2-70-sin-100-sin-20-

Question Number 149141 by mathdanisur last updated on 03/Aug/21

\frac{{c o s}^{2} (70) - {s i n}^{2} (70)}{s i n (100) + s i n (20)} = ?

Commented by liberty last updated on 03/Aug/21

= \frac{(\cos 70 ° - \sin 70 °) (\cos 70 ° + \sin 70 °)}{\sin 100 ° + \sin 20 °}

= \frac{(\sin 20 ° - \sin 70 °) (\sin 20 ° + \sin 70 °)}{2 \sin 60 ° \cos 40 °}

= \frac{2 \cos 45 ° \sin (- 25 °) (2 \sin 45 ° \cos 25}{\sqrt{3} \sin 50 °}

= \frac{- \sin 50 °}{\sqrt{3} \sin 50 °} = - \frac{1}{3} \sqrt{3}

Commented by mathdanisur last updated on 03/Aug/21

S e r, T h a n k Y o u