Question

For real vales of $\theta$, how many number of the following will be positive?
a. $\cos \left(\cos \theta \right)$
b. $\cos \left(\sin \theta \right)$
c. $\sin \left(\cos \theta \right)$
d. $\sin \left(\sin \theta \right)$

Answer 1

Given, $\theta$ belongs to Real numbers.
$\Rightarrow Sin\theta ,cos\theta ϵ[-1,1]$
1 Radian is equal to $\frac{180}{\pi }$degrees.
i.e.,The resultant values of $sin\theta ,cos\theta$ values lies either in Q1 or Q4.
Since cosine of positive or negative value is always positive.
$\Rightarrow cos\left(sin\theta \right),cos\left(cos\theta \right)$ will be always greater than zero.
Options A,B are correct.