CDS MATHEMATICS QUIZ 3

The value of $\frac{\sin 43^{\circ}}{\cos 47^{\circ}}+\frac{\cos 19^{\circ}}{\sin 71^{\circ}}-8 \cos ^{2} 60^{\circ}$ is.

The value of $\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}+\cot ^{2} 30^{\circ}$ is.

If $\sin 2 \theta=\frac{1}{2}$, then the value of $\cos \left(75^{\circ}-\theta\right)$ is.

The value of $\left(1+\sec 20^{\circ}+\cot 70^{\circ}\right) \times \left(1-\operatorname{cosec} 20^{\circ}+\tan 70^{\circ}\right)$ is.

IF $\sin \frac{\pi x}{2}=x^{2}-2 x+2$, then the value of $\mathrm{x}$ is.

In a right angled triangle $A B C, \angle B$ is the right angle and $A C=2 \sqrt{5} \mathrm{~cm}$. If $A B-B C=$ $2 \mathrm{~cm}$ then the value of $\left(\cos ^{2} A-\cos ^{2} C\right)$ is:

The minimum value of $2 \sin ^{2} \theta+3 \cos ^{2} \theta$ is.

IF $x \cos \theta-\sin \theta=1$, then $x^{2}-\left(1+x^{2}\right) \sin \theta$ equals.

Find the value of $\tan 4^{\circ} \tan 43^{\circ} \tan 47 \tan 86^{\circ}$.

The numerical value of $\frac{\cos ^{2} 45^{\circ}}{\sin ^{2} 60^{\circ}}+\frac{\cos ^{2} 60^{\circ}}{\sin ^{2} 45^{\circ}}-\frac{\tan ^{2} 30^{\circ}}{\cot ^{2} 45^{\circ}}-\frac{\sin ^{2} 30^{\circ}}{\cot ^{2} 30^{\circ}}$ is.