Trigonometric Ratio(sec,cosec,cot)

Q. Question 12
If $4tan\theta =3$, then $\left(\frac{4sin\theta -cos\theta }{4sin\theta +cos\theta }\right)$ is equal to

(A) $\frac{2}{3}$
(B) $\frac{1}{3}$
(C) $\frac{1}{2}$
(D) $\frac{3}{4}$

Q. What is the reciprocal of $cot\theta$?

1. $cos\theta$
2. $sin\theta$
3. $tan\theta$
4. $cosec\theta$

Q.

The value of (1 - Cos A)(1 + Cos A)($cose{c}^2$A) is __

Q. If $5sin\theta -12cos\theta =0$, find the values of $sec\theta$.

1. $\frac{12}{5}$
2. $\frac{12}{13}$
3. $\frac{13}{5}$
4. $\frac{5}{13}$

Q.

What is the value of cot B in terms of a, b, c?

1. $\frac{b}{a}$

2. $\frac{a}{b}$

3. $\frac{c}{b}$

4. $\frac{b}{c}$

Q. Which of the following is equal to $\cot \theta$?

1. $\frac{cos\theta }{sin\theta }$
2. $\frac{sin\theta }{tan\theta }$
3. $\frac{tan\theta }{sec\theta }$
4. $\frac{sin\theta }{cos\theta }$

Q. Find the value of $\sqrt{1+{\tan }^2\theta }\sqrt{1+{\cot }^2\theta }\sqrt{1-{\cos }^2\theta }\sqrt{1-{\sin }^2\theta }$.

Q.

If Sin A +Cosec A= 2, then $si{n}^2$A + $cose{c}^2$A =__

Q. If $sin\theta =\frac{a}{b},$ then find the value of $(sec\theta +tan\theta )$.

1. $\frac{b+a}{\sqrt{b^2-a^2}}$
2. $\frac{b+a}{\sqrt{b^2+a^2}}$
3. $\frac{b-a}{\sqrt{b^2+a^2}}$
4. $\frac{b-a}{\sqrt{b^2-a^2}}$

Q.

In triangle ABC, right-angled at B, if sin A =$\frac{12}{13}$, then find the value of

(sinA cosA + sinC cosC ).

1. $\frac{60}{169}$

2. $\frac{12}{13}$

3. $\frac{13}{12}$

4. $\frac{120}{169}$

Q. If $tan2A=cot(A-{18}^{\circ })$, where 2A is an acute angle, find the value of A.

Q.

In $△$PQR, PQ = 12 cm and PR = 13 cm. $\angle Q={90}^{\circ }$. Find tan P - cot R

1. $0$

2. $\frac{119}{60}$

3. $-\frac{119}{60}$

4. $1$

Q. In a right angled triangle ABC right angled at B,
$5\times sinA=3$.
Find the value of cosC + tanA + cosecC.

1. $\frac{12}{15}$
2. $\frac{13}{12}$
3. $\frac{13}{5}$
4. $\frac{12}{5}$

Q. If $sin\theta +cosec\theta =2$ then ${sin}^2\theta +{cosec}^2\theta$ is equal to

1. $4$
2. $1$
3. none
4. $2$

Q.

What is the value of tan θ in the given triangle?

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

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

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

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

Q. If $p\cot \theta =\sqrt{q^2-p^2}$, then find the value of $\sin \theta$.

Q. If $cosec\theta -\sin \theta =m$ and $\sec \theta -\cos \theta =n$, eliminate $\theta$.

1. ${\left(m^{2}n\right)}^{4/3}+{\left(m{n}^2\right)}^{4/3}=1$
2. ${\left(m^{4}n\right)}^{2/3}+{\left(m{n}^4\right)}^{2/3}=1$
3. ${\left(m^{3}n\right)}^{2/3}+{\left(m{n}^3\right)}^{2/3}=1$
4. ${\left(m^{2}n\right)}^{2/3}+{\left(m{n}^2\right)}^{2/3}=1$

Q. If $tan2A=cot(A-{18}^{\circ })$, where 2A is an acute angle, find the value of A.

Q.

ABDE is a trapezium.​​​​​​ with $AE\parallel BD$ and $ED\perp BD$, and AC is drawn parallel to the side DE

Find the values of $\text{cot}\theta \text{and}\text{cosec}\theta$ respectively, from the figure above.

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

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

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

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

Q.

What is the value of $sin\theta \times cosec\theta \times cot\theta =$ ?

1. $tan\theta$

2. $sin\theta$

3. $cot\theta$

4. $sec\theta$

Q. The value of $tan\theta \times cosec\theta \times cot\theta$ is ________ .

1. $cos\theta$
2. $tan\theta$
3. $cosec\theta$
4. $cot\theta$

Q. If $\tan \theta =\frac{10}{24}$, then $\sin \theta$ is equal to :

1. $\frac{24}{26}$
2. $\frac{26}{10}$
3. $\frac{10}{26}$
4. $\frac{10}{24}$

Q.

If 7 $si{n}^2\theta +3co{s}^2\theta =4$, then $sec\theta +cosec\theta$ is equal to

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

2. $\frac{2\sqrt{3}+6}{3}$

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

4. $\sqrt{3}$

Q. If $tan2A=cot(A-{18}^{\circ })$, where 2A is an acute angle, find the value of A.