Trigonometric Ratio(sin,cos,tan)

Q. If $Sin\theta =\frac{4}{5}$ and $Cos\theta =\frac{3}{5}$, then $tan\theta =$

1. $\frac{3}{5}$
2. $\frac{4}{5}$
3. $\frac{4}{3}$

Q. In PQR right angled at Q, QR=3 cm and PR -PQ =1 cm. determine thw values of sin R, cosR and tan R.

Q. If sec A = cosec B, then what is the value of A + B?

1. 50°
2. 90°
3. 180°
4. 120°

Q.

If $sin\theta =\frac{1}{\sqrt{2}}$, find all other trigonometric ratios of angle θ

Q.

In a triangle, $ABC,1-\tan \left(\frac{A}{2}\right)\tan \left(\frac{B}{2}\right)$ is equal to

1. $\frac{2c}{a+b+c}$

2. $\frac{2c}{a+b-c}$

3. $\frac{2b}{a+b+c}$

4. None of these

Q.

If in a $∆\mathrm{ABC}$, $A={\tan }^{-1}2$ and $B={\tan }^{-1}3$, then angle $C$ is

1. $\frac{\mathrm{\pi }}{2}$

2. $\frac{\mathrm{\pi }}{3}$

3. $\frac{\mathrm{\pi }}{4}$

4. None of these.

Q. If 16 cot x = 12, then what will be the value of $\frac{\sin x-\cos x}{\sin x+\cos x}$

Q. The value of $\frac{1-{\tan }^2{45}^{\circ }}{1+{\tan }^2{45}^{\circ }}=$

1. $1$
2. $\tan {90}^{\circ }$
3. $\sin {45}^{\circ }$
4. $0$

Q.

If $A+B+C=\pi$, $(A,B,C)>0$ and the angle $C$ is obtuse then

1. $\tan A\tan B>1$

2. $\tan A\tan B<1$

3. $\tan A\tan B=1$

4. None of these

Q. If A=30^°, prove sin3A=3sinA-4sinA

Q. In the given figure, find the length of BD.

1. 2 cm
2. 4 cm
3. 6 cm
4. 8 cm

Q.

In the given figure, is $sin\theta$ = $\frac{BC}{AC}$?

1. False

2. True

Q.

State whether the following statement is true or false. Justify your answer. The value of $\tan A$ is always less than $1$.

1. True
2. False

Q. 2tan3acos3a-tan3a+1=2cos3a; find the magnitude of a

Q.

If $\sec A=\frac{5}{4}$, verify that $\frac{3\sin A-4{\sin }^{3}A}{4{\cos }^{3}A-3\cos A}=\frac{3\tan A-{\tan }^{3}A}{1-3{\tan }^{2}A}$

Q.

The ratio (sinA + sinB): sin(A + B), when A = 60^o and B = 30^o is

1. 

2. 

3. 

4. 

Q.

Without using trigonometric tables, evaluate:

$\left(i\right)cos{48}^{\circ }-sin{42}^{\circ }$

$\left(ii\right)cosec{31}^{\circ }-sec{59}^{\circ }$

$\left(iii\right)cot{34}^{\circ }-tan{56}^{\circ }$

$\left(iv\right)co{s}^2{13}^{\circ }-si{n}^2{77}^{\circ }$ [4 MARKS]

Q. From the following figure, prove that $\theta +\varphi ={90}^{\circ }$. Also prove that there are two other right angled triangle. Find $\sin \alpha ,\cos \beta and\tan \varphi .$

Q. A right angled triangle $\Delta ABC$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find cosine of $\angle$B.

1. $\frac{7}{10}$
2. $\frac{4}{5}$
3. $\frac{3}{5}$
4. $\frac{6}{10}$

Q.

In given figure, if RP = 13 cm, QR = 5 cm and PS = 14 cm, then, tan S =

1. 

2. 

3. 

4. 

Q.

The angle ABC and BDC are right angles. If AD=9cm and DC=16cm and AB=15cm, then the length of BD is :

1. 12 cm

2. 16 cm

3. 15 cm

4. 25 cm

Q. If $\tan \theta =\frac{\cos 9^o+\sin 9^o}{\cos 9^o-\sin 9^o}$ then $\theta$ is equal to

1. ${54}^o$
2. ${18}^o$
3. $9^o$
4. ${36}^o$

Q. If $sin\theta =\frac{4}{5}$, find the value of $cos\theta$ and $tan\theta$ .

1. $\frac{3}{5},\frac{3}{4}$
2. $\frac{4}{5},\frac{3}{4}$
3. $\frac{3}{5},\frac{4}{3}$
4. $\frac{4}{5},\frac{4}{3}$

Q. Find the value of the $\frac{sin{17}^{\circ }sec{73}^{\circ }-cose{c}^2{67}^{\circ }}{se{c}^2{45}^{\circ }-tan{23}^{\circ }tan{67}^{\circ }+co{t}^2{67}^{\circ }}$

1. $co{s}^2{67}^{\circ }$
2. $-co{s}^2{67}^{\circ }$
3. $co{s}^2{73}^{\circ }$
4. $-co{s}^2{73}^{\circ }$

Q.

If $sin\theta =\frac{1}{\sqrt{2}}$, find all other trigonometric ratios of angle θ

Q. Question 13
Show that $\frac{co{s}^2({45}^{\circ }+\theta )+co{s}^2({45}^{\circ }-\theta )}{tan({60}^{\circ }+\theta )tan({30}^{\circ }-\theta )}=1$

Q. Find:
$\frac{\text{cos}{75}^{\circ }}{\text{sin}{15}^{\circ }}+\frac{\text{sin}{12}^{\circ }}{\text{cos}{78}^{\circ }}-\frac{\text{cos}{18}^{\circ }}{\text{sin}{72}^{\circ }}$

Q.

If $tan\theta =\frac{3}{4}$, find $sin\theta$.

1. $\frac{4}{5}$

2. $\frac{3}{5}$

3. $\frac{5}{4}$

4. $\frac{5}{3}$

Q.

$△$ ABC is right angled at B, perpendicular drawn to the opposite side AC bisects AC at D. BD = ___ cm if AD = DC = 5 cm.

Q. Find the value of
$\frac{co{t}^2{30}^{\circ }+8si{n}^2{45}^{\circ }+\frac{3}{2}se{c}^2{30}^{\circ }+2co{s}^2{90}^{\circ }}{2sec{60}^{\circ }+3cosec{30}^{\circ }-\frac{7}{3}ta{n}^2{60}^{\circ }}$