Relation between Trigonometric Ratios

Q.

Prove that $\frac{\cos \theta }{1+\sin \theta }=\frac{1-\sin \theta }{\cos \theta }$

Q.

If tan $\theta =\frac{a}{b}$, prove that $\frac{asin\theta -bcos\theta }{asin\theta +bcos\theta }=\frac{a^2-b^2}{a^2+b^2}$

Q.

The minimum value of $9{\tan }^2\theta +4{\cot }^2\theta$ is

1. $13$

2. $9$

3. $6$

4. $12$

Q.

$co{t}^{-1}\left(3\right)+\cos e{c}^{-1}(\surd 5)=$

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

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

3. $\frac{\mathrm{\pi }}{6}$

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

Q. Evaluate:

$\frac{\sin 30°}{\cos 45°}+\frac{\cot 45°}{\sec 60°}-\frac{\sin 60°}{\tan 45°}+\frac{\cos 30°}{\sin 90°}$

Q.

If sec $A=\frac{5}{4}$, verify that $\frac{3sinA-4si{n}^{3}A}{4co{s}^{3}A-3cosA}=\frac{3tanA-ta{n}^{3}A}{1-3ta{n}^{2}A}$

Q.

If tan $\theta =\frac{15}{8}$, find the values of all T-ratios of $\theta$

Q. If sin A = 3/5, what is the value of cos A?

1. 4/5
2. 4/9
3. 2/5
4. 1/5

Q.

In triangle $ABC,$ if $si{n}^{2}A+si{n}^{2}B+si{n}^{2}C=2$, then the triangle is

1. Right angle but need not be isosceles

2. Right angled and isosceles

3. Isosceles but need not be right angled

4. Equilateral

Q.

If sin $\theta =\frac{a^2-b^2}{a^2+b^2}$, find the values of all T-ratios of $\theta$

Q.

What are the $3$ trigonometric identities?

Q.

$\cos c+\cos d$ is equal to

Q.

What is the value of $\cos ec30°$?

Q.

For what value of $x$, the complex numbers $\sin x+i\cos 2x$ and $\cos x-i\sin 2x$ are conjugate to each other.

1. $x=npi$

2. $x=\left(n+\frac{1}{2}\right)pi$

3. $x=0$

4. No values of $x$

Q. If A = 60° and B = 30°, verify that:

(i) sin (A − B) = sin A cos B − cos A sin B
(ii) cos (A − B) = cos A cos B + sin A sin B
(iii) tan (A − B) = $\frac{\tan A-\tan B}{1+\tan A\tan B}$

Q.

$\frac{sinA-sinB}{cosA+cosB}+\frac{cosA-cosB}{sinA+sinB}=$

1. - 1

2. 0

3. 1

4. 2

Q.

If sin A = $\frac{9}{41}$, find the values of cos A and tan A,

Q. If $2{\sin }^2\mathrm{\theta }-{\cos }^2\mathrm{\theta }=2$ , then find the value of $\mathrm{\theta }$ .

Q.

If cosec $\theta =2$, show that $cot\theta +\frac{sin\theta }{1+cos\theta }$ = 2.

Q. If 8 tan x = 15, then sin x − cos x is equal to

(a) $\frac{8}{17}$
(b) $\frac{17}{7}$
(c) $\frac{1}{17}$
(d) $\frac{7}{17}$

Q.

If cot $\theta =2$, find the values of all T-ratios of $\theta$.

Q.

Find the value of $\cos 2\theta ,$if $2\sin 2\theta =\sqrt{3}.$

Q.

If $\sec \theta =\frac{17}{8}$, verify that $\frac{3-4si{n}^2\theta }{4co{s}^2\theta -3}=\frac{(3-ta{n}^2\theta )}{(1-3ta{n}^2\theta )}$.

Q.

If 3 tan $\theta$=4, find the value of $\frac{4cos\theta -sin\theta }{2cos\theta +sin\theta }$

Q.

If $\sin \left(\theta \right)+\mathrm{cosec}\left(\theta \right)=2$, then ${\sin }^2\left(\theta \right)+{\mathrm{cosec}}^2\left(\theta \right)=$

1. $1$

2. $4$

3. $2$

4. None of these

Q.

If $se{c}^2\theta =\frac{4}{3}$, then the general value of $\theta$ is

1. $2n\mathrm{\pi }\pm \frac{\mathrm{\pi }}{6}$

2. $n\mathrm{\pi }\pm \frac{\mathrm{\pi }}{6}$

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

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

Q.

In a D ABC, right angled at A, if tan $C=\sqrt{3}$, find the value of sin B cos C + cos B sin C.

Q.

If $-1+\sqrt{-3}=r{e}^{\iota \theta }$, then $\theta$ is equal

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

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

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

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

Q.

Solve the following:

(i)cos 225°+sin165°

Q.

If $|a\times b{|}^2+|a.b{|}^2=144$ and $\left|a\right|=4$, then $\left|b\right|$ is equal to?

1. $16$

2. $8$

3. $3$

4. $12$