Trigonometric Ratios of Standard Angles

Q. $\frac{1-ta{n}^2{45}^{\circ }}{1+ta{n}^2{45}^{\circ }}=$

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

Q. Question 1
If $cosA=\frac{4}{5}$, then the value of tan A is

(A) $\frac{3}{5}$
(B) $\frac{3}{4}$
(C) $\frac{4}{3}$
(D) $\frac{5}{3}$

Q.

If $bcos\theta =a$, then prove that

$cosec\theta +cot\theta =\sqrt{\frac{b+a}{b-a}}$ [4 MARKS]

Q. Question 9
If $sinA+si{n}^{2}A=1$, then the value of $(co{s}^{2}A+co{s}^{4}A)$ is

(A) $1$
(B) $\frac{1}{2}$
(C) $2$
(D) $3$

Q. Question 7
If $cos9\alpha =sin\alpha$ and $9a<{90}^{\circ }$, then the value of $tan5\alpha$ is

(A) $\frac{1}{\sqrt{3}}$
(B) $\sqrt{3}$
(C) $1$
(D) $0$

Q.

Given that cos θ = ^m/_n then tanθ is equal to

1. 

2. 

3. 

4. 

Q.

What is sin$\theta$ $\times$ cos$\theta$ $\times$ sec$\theta$ $\times$ cot$\theta$ ?

Q.

Find the value of sin(60+$\theta$) - cos(30-$\theta$).

1. 2 cos$\theta$

2. 2 sin$\theta$

3. 0

4. 1

Q.

$△PQR$, right-angled at Q, if PR = 24cm, QR = 12cm, then find the value of $\angle QRP$.

1. 45^o

2. 90^o

3. 30^o

4. 60^o

Q.
ABCD is a rectangle such that $\angle CAB={60}^{\circ }$ and $AC=aunits$.
Find the area of rectangle ABCD.

1. $\frac{\sqrt{3}}{2}{a}^2$

2. $\frac{\sqrt{2}}{3}{a}^2$

3. $\frac{\sqrt{3}}{4}{a}^2$
4. $\frac{\sqrt{3}}{8}{a}^2$

Q.

If the diagonal of the given square is 4 cm, find its perimeter and area.

Q.

Find the value of $\theta :$

$\tan \theta =\sin 45°\cos 45°+\sin 30°$

Q. Question 2 (iv)
Choose the correct option and justify your choice.
(iv) $\frac{2tan30^0}{1-ta{n}^2{30}^0}=$
(A) $cos{60}^{\circ }$
(B) $sin{60}^{\circ }$
(C) $tan{60}^{\circ }$
(D) $sin{30}^{\circ }$

Q. The diagonal of a rectangle is 12 cm and makes an angle ${35}^{\circ }$ with one side .Then find the area of the rectangle. $[sin{35}^{\circ }=0.57,cos{35}^{\circ }=0.81]$

Q. Question 3 (i)
Evaluate:
(i)$\frac{(si{n}^2{63}^{\circ }+si{n}^2{27}^{\circ })}{(co{s}^2{17}^{\circ }+co{s}^2{73}^{\circ })}$

Q. In $△$ PQR , $\angle$ Q = ${90}^{\circ }$. If cot ~P = $\sqrt{3}$ then, find $\frac{sinP+cosR}{tanR}$.

1. $\frac{1}{\sqrt{6}}$
2. $\frac{1}{\sqrt{3}}$
3. $\sqrt{3}$
4. $\frac{2}{\sqrt{3}}$

Q.

If tan 2A = cot (A-${18}^{\circ }$), then find the value of A.

1. ${18}^{\circ }$

2. ${36}^{\circ }$

3. ${24}^{\circ }$

4. ${27}^{\circ }$

Q. If $0<\theta <90$ and $2\sin 2\theta =\sqrt{3},$ then find the value of $\theta .$

Q. Question 2 (ii)
Choose the correct option and justify your choice.
(ii) $\frac{1-ta{n}^2{45}^0}{1+ta{n}^2{45}^0}=$
(A) $tan{90}^{\circ }$
(B) 1
(C) $sin{45}^{\circ }$
(D) 0

Q.

Which of the following statements is true for $\theta$ ranging from $0^{\circ }$ to ${90}^{\circ }$?

1. $cos\theta ,cot\theta andcosec\theta$ increases as $\theta$ increases.

2. $sin\theta =cos\theta$ for all the values of $\theta$

3. Trigonometric ratios values do not follow any pattern.

4. $sin\theta ,tan\theta andsec\theta$ increases as $\theta$ increases.

Q.

For a triangle ABC, show that sin$\left(\frac{B+C}{2}\right)$ = cos $\left(\frac{A}{2}\right)$ , where A, B and C are interior angles of $△$ ABC.

Q. In $△ABC$ , $\angle B={90}^{\circ }$.

If $cotA=\frac{1}{\sqrt{3}}$ then,

find $\frac{cosA}{sinA}+\frac{sinC}{cosC}$

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

Q. If $x=\frac{2sin\theta }{1+sin2\theta +cos2\theta }$ and $\theta =45°,$ then find the value of $x$.

1. $\sqrt{2}$
2. $\frac{1}{\sqrt{2}}$
3. $2$
4. $0$

Q.

In $△$ABC, right angled at B, BC = 5cm, $\angle BAC$ = ${30}^{\circ }$, find the length of the sides AB and AC.

Q. At $\theta$ = ${60}^{\circ }$, the value of sec $\theta$ + cosec $\theta$ is ____.

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

Q. Question 11
The value of the expression
$(\frac{si{n}^2{22}^{\circ }+si{n}^2{68}^{\circ }}{co{s}^2{22}^{\circ }+co{s}^2{68}^{\circ }}+si{n}^2{63}^{\circ }+cos{63}^{\circ }{27}^{\circ })$ is

(A) 3
(B) 2
(C) 1
(D) 0

Q.

$\frac{sin({90}^{\circ }-\theta )cos({90}^{\circ }-\theta )}{cot({90}^{\circ }-\theta )}$ + $si{n}^2\theta$ =

__

Q. ABCD is a rectangle such that $\angle CAB=60°$ and AC = $a$ units. The area of rectangle ABCD is _______.

1. $\frac{\sqrt{2}}{3}{a}^2$ sq. units
2. $\frac{\sqrt{3}}{2}{a}^2$ sq. units
3. $\frac{\sqrt{3}}{4}{a}^2$sq. units
4. $\frac{\sqrt{3}}{8}{a}^2$ sq. units

Q.

Most of the trigonometric ratios are unrelated.

1. False

2. True

Q. If $sin\alpha =cos(90°-\beta )=\frac{1}{\sqrt{2}}$ and $0°\le \alpha ,\beta \le 90°$, then find $\alpha +\beta$.

1. 30°
2. 90°
3. 60°
4. 45°