Find-1-sin-10-4-sin-70-

Question Number 185668 by Shrinava last updated on 25/Jan/23

Find : \frac{1}{\sin 10 °} - 4 \sin 70 ° = ?

Answered by Ezzat last updated on 25/Jan/23

= \frac{1 - 4 s i n 10 ° s i n 70 °}{s i n 10 °}

= \frac{1 - 4 \times \frac{1}{2} (c o s (10 ° - 70 °) - c o s (10 ° + 70 °))}{s i n 10 °}

= \frac{1 - 2 (c o s (60 °) - c o s 80 °)}{s i n 10 °}

= \frac{1 - 2 (\frac{1}{2} - c o s 80 °)}{s i n 10 °}

= \frac{1 - 1 + 2 c o s 80 °}{s i n 10 °}

= 2 \frac{c o s 80 °}{c o s 80 °} = 2

Answered by greougoury555 last updated on 25/Jan/23

\frac{1 - 4 \sin 70 ° \sin 10 °}{\sin 10 °}

= \frac{1 + 2 (\cos 80 ° - \cos 60 °)}{\sin 10 °}

= 2