Trigonometric Ratios of Allied Angles

Q.

The value of ${\sin }^2{5}^{\circ }+{\sin }^2{10}^{\circ }+{\sin }^2{15}^{\circ }+$..............

$+{\sin }^2{85}^{\circ }+{\sin }^2{90}^{\circ }$ is equal to

1. $7$

2. $8$

3. $9$

4. $\frac{19}{2}$

Q.

Find the value of other five trigonometric functions if cot x = $\frac{3}{4}$, and x lies in third quadrant.

Q.

Q. $\frac{\cos 10°+\sin 10°}{\cos 10°-\sin 10°}=$

(a) tan 55°
(b) cot 55°
(c) −tan 35°
(d) −cot 35°

Q. . If tanA-tanB=x & cotB-cotA=y, then prove that cot(A-B) =1/x + 1/y

Q. Find the derivative of the following function:
f(x) = $\frac{x}{si{n}^{n}x}$

Q.

sin( 75^o)

1. 

2. 

3. 

4. 

Q.

${\sin }^2{5}^{\circ }+{\sin }^2{10}^{\circ }+{\sin }^2{15}^{\circ }+...+{\sin }^2{85}^{\circ }+{\sin }^2{90}^{\circ }=$

1. $9\frac{3}{4}$
2. $8$
3. $9$
4. $9\frac{1}{2}$

Q. Find the derivative of $\cos x$ by first principle.

Q. 39. If cos θ = 5/13, then find the value of θ.

Q.

The value of $si{n}^2{5}^{\circ }+si{n}^2{10}^{\circ }+si{n}^2{15}^{\circ }$ + ..............+

$si{n}^2{85}^{\circ }+si{n}^2{90}^{\circ }$ is equal to

[Karnataka CET 1999]

1. 8

2. 9

3. 

4. 7

Q. 2 3π44

Q. 35. Tan(/4+A)-tan(/4-A) equal to 1.2tanA 2.2tan2A 3.tan2a

Q.

What is the value of cosθ/2?

1. 

2. 

3. 

4. 

Q. Prove that:
$\sin 36°\sin 72°\sin 108°\sin 144°=\frac{5}{16}$

Q. Prove that:
(i) sin 38° + sin 22° = sin 82°
(ii) cos 100° + cos 20° = cos 40°
(iii) sin 50° + sin 10° = cos 20°
(iv) sin 23° + sin 37° = cos 7°
(v) sin 105° + cos 105° = cos 45°
(vi) sin 40° + sin 20° = cos 10°

Q. The value of $\sin {40}^{\circ }{35}^{\prime }\cos {19}^{\circ }{25}^{\prime }+\cos {40}^{\circ }{35}^{\prime }\sin {19}^{\circ }{25}^{\prime }$ is

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

Q.

How do you evaluate $\sec \left(\mathrm{\pi }\right)$?

Q. The value of sin 78° − sin 66° − sin 42° + sin 60° is
(a) $\frac{1}{2}$

(b) $-\frac{1}{2}$

(c) −1

(d) None of these

Q. Evaluate $\frac{\cos {65}^{\circ }\sin {18}^{\circ }\cos {58}^{\circ }}{\cos {72}^{\circ }\sin {25}^{\circ }\sin {32}^{\circ }}$

Q.

The quadratic equation $\tan \theta x^2+2(\sec \theta +\cos \theta )x+(\tan \theta +3\sqrt{2}\cot \theta )$ always has

1. equal roots for all $\theta$

2. complex roots for all $\theta$

3. real and distinct roots for all $\theta$

4. real roots or complex roots depending upon $\theta$

Q. $\sin (-\theta )+\cos (-\theta )+\sec (-\theta )+\sin (\pi -\theta )+\cos (\pi -\theta )+\sec (\pi -\theta )=$

1. $2\sin \theta$
2. $2\cos \theta$
3. $2\sec \theta$
4. $0$

Q. Find the value of cos Ө + cos(2 Π/3+ Ө )+ cos (2 Π/3- Ө )

Q. $\mathrm{Prove}\mathrm{that}4\cos \mathrm{\theta }\cos \left(\frac{\mathrm{\pi }}{3}+\mathrm{\theta }\right)\cos \left(\frac{\mathrm{\pi }}{3}-\mathrm{\theta }\right)=\cos 3\mathrm{\theta }.$

Q.

(i) If sin $x=\frac{1}{3}$, find the value of sin $3x$

(ii) If cos $x=\frac{1}{2}$, find the value of cos $3x$

Q. Prove that:
$\sec \left(\frac{3\mathrm{\pi }}{2}-x\right)\sec \left(x-\frac{5\mathrm{\pi }}{2}\right)+\tan \left(\frac{5\mathrm{\pi }}{2}+x\right)\tan \left(x-\frac{3\mathrm{\pi }}{2}\right)=-1.$

Q. 22.2sin2_+ cosec

Q. Prove the following:
$\frac{cos9x-cos5x}{sin17x-sin3x}=-\frac{sin2x}{cos10x}$

Q. range of sec^2x-†an x+1/(sec^2x+†an x+1

Q. Eliminate θ between the relations tanθ+sinθ=p and tanθ−sinθ=q