CDS TRIGONOMETRY QUIZ 30

Question 1:

Find the value

$\frac{5 \sin ^{2} 30+\cos ^{2} 45^{\circ}-4 \tan ^{2} 30^{\circ}}{2 \sin 30^{\circ} \cos 30^{\circ}+\tan 45^{\circ}}$ is

$\frac{5}{6}(2-\sqrt{3})$

$\frac{5}{6}(2+\sqrt{3})$

$2-\sqrt{3}$

$\frac{1}{6}(2-\sqrt{3})$

Question 2:

If $\cos A+\cos ^{2} A=1$ and $a \sin ^{12} A+b \sin ^{10} A+$ $c \sin ^{8} A+d \sin ^{6} A-1=0$. Find the vlaue of $\mathrm{a}+\frac{b}{c}+\mathrm{d}$

4

0

1

3

Question 3:

If $\sin ^{2}\left(37^{\circ}-3 x\right)+\cos ^{2}\left(3 y-23^{\circ}\right)=1$, then find the value of $\tan 6(x+y)=?$

1

$\frac{-1}{\sqrt{3}}$

$-\sqrt{3}$

$\sqrt{3}$

Question 4:

If $\sin ^{4} \theta+8 \cos ^{2} \theta=4$, then find the vlaue of $\sin ^{2} \theta-2 \sin \theta$

2

-2

1

-1

Question 5:

If $\sin ^{2} 35^{\circ}+\cos ^{2}\left(3 x-25^{\circ}\right)=1$, then find the value of $\tan 3 x+\cos 3 x $

$\frac{2 \sqrt{3}+1}{2}$

$\frac{3 \sqrt{2}+1}{2 \sqrt{2}}$

$\frac{2 \sqrt{3}+1}{4}$

None of these

Question 6:

If $\tan 3 \theta=\cot 6 \theta$, find $\sin 3 \theta+\cos 6 \theta$ ?

$0$

$1$

$-1$

$\frac{1}{2}$

Question 7:

find $\frac{\cos ^{3} \theta+3 \cos 2 \theta}{\cos ^{6} \theta-\sin ^{6} \theta}=?$

0

1

2

4

Question 8:

Find the value of $\sin 79^{\circ} \sec 11^{\circ}+\sin 11^{\circ} \sec 79^{\circ}$

$1$

$\frac{1}{2}$

$2$

$\frac{1}{\sqrt{2}}$

Question 9:

If $\tan \mathrm{A}+\cot \mathrm{A}=4$, then $\tan ^{4} \mathrm{~A}+\cot ^{4} \mathrm{~A}$ is

equal to:-

110

191

80

194

Question 10:

Direction: Convert the decimal degrees to degree, minutes and seconds.

$23.45^{\circ}$

$23^{\circ} 26^{\prime}$

$24^{\circ} 25^{\prime}$

$23^{\circ} 27^{\prime}$

$22^{\circ} 8^{\prime}$