CDS TRIGONOMETRY QUIZ 29

Question 1:

The value of $\frac{\cos ^{3} 20^{\circ}-\cos ^{3} 70^{\circ}}{\sin ^{3} 70^{\circ}-\sin ^{3} 20^{\circ}}=$ ?

5

7

1

3

Question 2:

If $3 \sin \theta+4 \cos \theta=5$ then find the value of' $\tan \theta$ '

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{6}{5}$

Question 3:

If $\sin \alpha \cdot \sec \left(30^{\circ}+\alpha\right)=1\left(0<\alpha<60^{\circ}\right)$, then find the value of $(\sin \alpha+\cos 2 \alpha)$

$1$

$\frac{2+\sqrt{3}}{2 \sqrt{3}}$

$0$

$\sqrt{2}$

Question 4:

Find the value of $\tan 225^{\circ} \cot 405^{\circ}+\tan$ $765^{\circ} \cot 675^{\circ}$

0

1

$\frac{1}{2}$

$\frac{-\sqrt{3}}{2}$

Question 5:

If $\sin (\mathrm{A}+\mathrm{B})=\frac{\sqrt{3}}{2}$ and $\sin (\mathrm{A}-\mathrm{B})=\frac{1}{2}, \mathrm{0}^{\circ}<$ $A, B<90^{\circ}$ then find $A, B$

$45^{\circ}, 15^{\circ}$

$20^{\circ}, 30^{\circ}$

$15^{\circ}, 45^{\circ}$

$60^{\circ}, 90^{\circ}$

Question 6:

Find the value $\frac{\sin 30^{\circ}+\tan 45^{\circ}-\operatorname{cosec} 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}$

$\frac{21-8 \sqrt{3}}{11}$

$\frac{26+8 \sqrt{6}}{22}$

$\frac{43-24 \sqrt{3}}{11}$

None of these

Question 7:

If $\sin \theta+\cos \theta=\frac{23}{17}$, find $\sin \theta \cos \theta=?$

$\frac{240}{289}$

$\frac{17}{23}$

$\frac{120}{289}$

$\frac{120}{17}$

Question 8:

Find the value of $\frac{\tan 1^{\circ}}{1+\tan 1^{\circ}}+\frac{\tan 2^{\circ}}{1+\tan 2^{\circ}}+\ldots . .+\frac{\tan 89^{\circ}}{1+\tan 89^{\circ}}$

$23.5$

$44.5$

$43.5$

$41.5$

Question 9:

If $x \sin 45^{\circ}=y \operatorname{cosec} 30^{\circ}$, then $\frac{x^{4}}{y^{4}}$ is equal to:

81

64

72

84

Question 10:

If $\sin \theta+\operatorname{cosec} \theta=2$, then find the value of $\sin ^{5} \theta+\operatorname{cosec}^{5} \theta$