Standard Values of Trigonometric Ratios

Q.

Using the formula, $tan2A=\frac{2tanA}{1-ta{n}^2{A}^{\prime }}$ find the value of $tan{60}^{\circ },$ it being given that $tan{30}^{\circ }=\frac{1}{\sqrt{3}}.$

Q. If sin3A=cos(A-26°), where 3A is an acute angle find the value of A.

Q.

If A and B are acute angles such that tan $A=\frac{1}{2},tanB=\frac{1}{3}$ and tan $(A+B)=\frac{tanA+tanB}{1-tanAtanB}$, find A + B

Q.

Cos theta+sin theta =√2cos theta show thatcos theta-sin theta =√2sin theta

Q.

Express the trigonometric ratios sin A , sec A and tan A in terms of cot A

Q.

The value of tan6*tan42*tan66*tan78 is

Q. SinA+sinB=a and cosA-cosB=b then tan(A-B)/2?

Q.

$\cos \left[2{\cos }^{-1}\left(\frac{1}{5}\right)+{\sin }^{-1}\left(\frac{1}{5}\right)\right]=?$

1. $\frac{2\sqrt{6}}{5}$

2. $\frac{-2\sqrt{6}}{5}$

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

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

Q.

Prove that sin2A is equal to 2sinAcosA

Q. $\text{If}sin\theta =\frac{1}{2}$
and $\theta$ is acute,
$\text{then find the value of}(3cos\theta -4co{s}^3\theta ).$

1. $0$
2. $\frac{1}{2}$
3. $\frac{1}{6}$
4. $-1$

Q. In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

(i) $\sin A=\frac{2}{3}$
(ii) $\cos A=\frac{4}{5}$
(iii) tan θ = 11
(iv) $\sin \theta =\frac{11}{15}$
(v) $\tan \mathrm{\alpha }=\frac{5}{12}$
(vi) $\sin \theta =\frac{\sqrt{3}}{2}$
(vii) $\cos \theta =\frac{7}{25}$
(viii) $\tan \theta =\frac{8}{15}$
(ix) $\cot \theta =\frac{12}{5}$
(x) $\sec \theta =\frac{13}{5}$
(xi) $\mathrm{cosec}\mathrm{\theta }=\sqrt{10}$
(xii) $\cos \theta =\frac{12}{15}$

Q.

Show that:

(i) $\frac{1-\sin {60}^{\circ }}{\cos {60}^{\circ }}=\frac{\tan {60}^{\circ }-1}{\tan {60}^{\circ }+1}$

(ii) $\frac{\cos {30}^{\circ }+\sin {60}^{\circ }}{1+\sin {30}^{\circ }+\cos {60}^{\circ }}=\cos {30}^{\circ }$

Q.

Evaluate each of the following

cos${60}^{\circ }$ cos${45}^{\circ }$ - sin ${60}^{\circ }$ sin ${45}^{\circ }$

Q.

Find the value of

$\frac{1-ta{n}^2{30}^{\circ }}{1+ta{n}^2{30}^{\circ }}$

1. 2

2. 4

3. 0.5

4. 1

Q.

The value of sin² 30^o - cos² 30^o is :

1. 

2. 

3. 

4. 

Q.

If sin (A + B) = 1 and cos (A - B) = 1, $0^{\circ }\le (A+B)\le {90}^{\circ }$ and A > B then find A and B.

Q.

If A + B + C = $\pi ,$ the maximum value of cos A + cos B + cos C can have is --

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

Q.

If A = ${45}^{\circ },$ verify that:

(i) $sin2A=2sinAcosA$ (ii) $cos2A=2co{s}^{2}A-1=1-2si{n}^{2}A$

Q.

If cos x = cos 60^o cos 30^o + sin 60^o sin 30^o, then the value of x is

1. 15^o

2. 45^o

3. 30^o

4. 60^o

Q.

The maximum value of $3\cos \left(x\right)+4\sin \left(x\right)+5$ is

1. $5$

2. $6$

3. $7$

4. None of these

Q.

Given that sin(A+B)=sinA cosB+cosA sinB, find the value of sin75°

Q.

What is the value of sin 60 - cos 30

Q.

If $\angle A$ and $\angle P$ are acute angles such that tan A = tan P, then show that $\angle A=\angle P$

Q.

Given that sin A= $\frac{1}{2}$ and cosB =$\frac{1}{\sqrt{2}}$, then find the value of (A+B) (where A and B are acute angles).

1. 30°

2. 45°

3. 75°

4. 15°

Q.

The value of cos² 17^o – sin² 73^o is

1. 3

2. 0

3. -1

4. 1

Q. If SecA + tanA = x. Find secA-tanA in terms of x.

Q.

What is the value of $\frac{\sin {45}^{\circ }\sin {30}^{\circ }}{\cos {45}^{\circ }\cos {30}^{\circ }}$?

Q.

If $A+B+C=270°$, then $\cos 2A+\cos 2B+\cos 2C+4\sin \left(A\right)\sin \left(B\right)\sin \left(C\right)=?$

1. $0$

2. $1$

3. $2$

4. $3$

Q. For triangle ABC, show that. SIN A+B/2=COS C/2

Q.

Sin 65/cos 25 + cos32/sin58 - sin28 × sec 62 + cosec^​​2​30 = ?

Plz note they are degrees. Thank you