Trigonometry - Mathematics Previous Year Questions

If \(\theta=\frac{\pi}{2^n+1}\), then the value of \(2^n \cos \theta \cos 2 \theta \cos 2^2 \theta \ldots \cos 2^{n-1} \theta\) is

If \(0< a<5,0< b<5\) and \(\frac{x^2+5}{2}=x-2[\cos (a+b x)]\) is satisfied for atleast one real \(x\), then the least value of \(\frac{a+b}{\pi}\) is equal to

The minium value of \(\left[2-\cos \theta+\sin ^2 \theta\right]\) is

$\tan 65^{\circ}, \tan 40^{\circ}+\tan 25^{\circ}$ and $\tan 25^{\circ}$ are in

The value of \(\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left\{\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right\}\) is

\(\cos (x+y), \cos x, \cos (x-y)\) are in HP, then \(\cos x \sec \frac{y}{2}\) is