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. None if these

Answer 1

Answer: (B)

$1$

$\frac{1-4sin{10}^{o}sin{70}^o}{2son{10}^o}=\frac{1-4sin{10}^{o}sin(90-20)}{2sin{10}^o}$

$\frac{1-4sin{10}^{o}cos{20}^o}{2sin{10}^o}$ $\left\{sincesin\right(90-\theta )=cos\theta$

$\frac{1-2\left(sin{10}^{o}cos{20}^o\right)}{2sin{10}^o}$

$\frac{1-2sin30+sin(-{10}^o)}{2sin{10}^o}$ $\left\{sincesin\right(A+B)+Sin(A-B)=2SinACosB$

$\frac{1-2(1/2-sin{10}^o)}{2sin{10}^o}$

$\frac{1-2\times \frac{1}{2}+2sin{10}^o)}{2sin{10}^o}=1$