Question

The value of the expression
$\frac{1-4\sin {10}^{\circ }\sin {70}^{\circ }}{2\sin {10}^{\circ }}$ is

• A. $\frac{1}{2}$
• B. $1$
• C. $2$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$1$

$1-4\sin 10\sin 70=1-2(\cos 60-\cos 80)=1-2\cos 60+2\cos 80=2\cos 80=2\sin 10$

$\therefore \frac{1-4\sin {10}^{\circ }\sin {70}^{\circ }}{2\sin {10}^{\circ }}=\frac{2\sin 10}{2\sin 10}=1$
Hence the answer is $1$