CDS TRIGONOMETRY QUIZ 32

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Question 1:

Find the value.

 $\left[\tan ^{2}(90-\theta)-\sin ^{2}(90-\theta)\right] \operatorname{cosec}^{2}(90-\theta) \cdot \cot ^{2}(90-\theta)]$

Question 2:

If $A+B+C=90^{\circ}$ then find the value of $\tan A \cdot \tan B+\tan B \cdot \tan C+\tan C \cdot \tan A$

Question 3:

Find the value.

$\tan 15^{\circ} \cdot \tan 65^{\circ}+\tan 65^{\circ} \cdot \tan 10^{\circ}+\tan 10^{\circ} \cdot \tan 15^{\circ}$?

Question 4:

If $2 y \cos \theta=x \sin \theta$ and $2 x \sec \theta-y \operatorname{cosec} \theta=3$ then find the value of $x^{2}+4 y^{2}=?$

Question 5:

In a $\Delta \mathrm{ABC}$, if $\mathrm{a}^{2}, \mathrm{~b}^{2}, \mathrm{c}^{2}$ are in A.P, then find $\cot A, \cot B, \cot C$ are in $\ldots . . .$

Question 6:

Find the value.

$\frac{(\sin x+\sin y)(\sin x-\sin y)}{(\cos x+\cos y)(\cos y-\cos x)}$

Question 7:

The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.

Question 8:

Find the value

$\left(1-2 \sin ^{2} \theta\right)\left(\frac{1+\tan \theta}{1-\tan \theta}+\frac{1-\tan \theta}{1+\tan \theta}\right) \text { where, } 0 \leq \theta \leq 90$

Question 9:

If $\tan \theta+\cot \theta=2$, then find the value of $\tan ^{2} \theta+\cot ^{2} \theta$?

Question 10:

Find the value of

$\sqrt{3} \tan 10^{\circ}+\sqrt{3} \tan 20^{\circ}+\tan 10^{\circ} \tan 20^{\circ}$