Question

The value of ${\cos }^2{10}^o-\cos {10}^o\cos {50}^o+{\cos }^2{50}^o$ is?

• A. $\frac{3}{2}(1+\cos {20}^o)$
• B. $\frac{3}{4}$
• C. $\frac{3}{4}+\cos {20}^o$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$\frac{3}{4}$

$\frac{1}{2}(2{\cos }^2{10}^o-2\cos {10}^o\cos {50}^o+2{\cos }^2{50}^o)$
$\Rightarrow \frac{1}{2}(1+\cos {20}^o-(\cos {60}^o+\cos {40}^o)+1+\cos {100}^o)$
$\Rightarrow \frac{1}{2}(\frac{3}{2}+\cos {20}^o+2\sin {70}^o\sin (-{30}^o\left)\right)$
$\Rightarrow \frac{1}{2}(\frac{3}{2}+\cos {20}^o-\sin {70}^o)$
$\Rightarrow \frac{1}{2}(\frac{3}{2}+\sin {70}^o-\sin {70}^o)$
$\Rightarrow \frac{3}{4}$ Ans. $\left(2\right)$.