Question

The expression $2cos{10}^o+sin{100}^o+sin{1000}^o+sin{10000}^o$ is simplified, then it simplifies to?

Answer 1

Given

$2\cos {10}^o+\sin {100}^o+\sin {1000}^o+\sin {10000}^o$

By using trigeometric property

$\sin (\frac{n\pi }{2}+\theta )=\cos \theta$ [there $n=odd$]

we get

$\Rightarrow 2\cos {10}^o+\sin (90+{10}^o)+\sin (90\times 11+{10}^o)+\sin (90\times 111+{10}^o)$

$\Rightarrow 2\cos {10}^o+\cos {10}^o+\cos {10}^o+\cos {10}^o$

$\Rightarrow 5\cos {10}^o$