Phrases Trigonometry Previous Year Question Paper and Solution with PDF

Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations

Phrases
Previous Year Questions

Phrases
Previous Year Questions
Phrases

Phrases Previous Year Questions (PYQs)

Phrases Trigonometry PYQ

Qus : 1

The expression

$\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$ can be written as

1
2
3
4
Go to Discussion

Solution

Qus : 2

Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60°, respectively. The ratio of AB and BC is

1
2
3
4
Go to Discussion

Solution

According to the given information, the figure should be as follows.

Let the height of tower = h

Qus : 3

$3 sin x + 4 cos x = 5$ , then

$6tan\frac{x}{2}-9tan^2\frac{x}{2}$

1
2
3
4
Go to Discussion

Solution

Qus : 4

Largest value of

$cos^2\theta -6sin\theta cos\theta+3sin^2\theta+2$ is

1
2
3
4
Go to Discussion

Solution

Qus : 5

Number of point of which f(x) is not differentiable

$f(x)=|cosx|+3$ in

$[-\pi, \pi]$

1
2
3
4
Go to Discussion

Solution

Points of Non-Differentiability of $f(x) = |\cos x| + 3$

Step 1: $\cos x$ is differentiable everywhere, but $|\cos x|$ is not differentiable where $\cos x = 0$ .

Step 2: In the interval $[-\pi, \pi]$ , we have:

$\cos x = 0 \Rightarrow x = -\frac{\pi}{2},\ \frac{\pi}{2}$

So $f(x) = |\cos x| + 3$ is not differentiable at these two points due to sharp turns.

✅ Final Answer: $\boxed{2 \text{ points}}$

Qus : 6

If A > 0, B > 0 and A + B =

$\frac{\pi}{6}$ , then the minimum value of

$tanA + tanB$

1
2
3
4
Go to Discussion

Solution

On differentiating

x= tanA + tan(π/6-A)

we get :

dx/dA = sec²A-sec²(π/6-A)

now putting

dx/dA=0

we get

cos²(A) = cos²(π/6-A) so 0≤A≤π/6

therefore

A=π/6-A from here we get A = π/12 = B

so minimum value of that function is

2tanπ/12 which is equal to 2(2-√3)

Qus : 7

The

$sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx$ ,

$x \in (0 , \pi)$ , then x

1
2
3
4
Go to Discussion

Solution

Qus : 8

$cosec\theta-cot \theta=2$ , then the value of

$cosec\theta$ is

1
2
3
4
Go to Discussion

Solution

Qus : 9

The solution of the equation

${4\cos }^2x+6{\sin }^2x=5$ are

1
2
3
4
Go to Discussion

Solution

Qus : 10

The value of

$\tan \Bigg{(}\frac{\pi}{4}+\theta\Bigg{)}\tan \Bigg{(}\frac{3\pi}{4}+\theta\Bigg{)}$ is

1
2
3
4
Go to Discussion

Solution

We are given:

$\text{Evaluate } \tan\left(\frac{\pi}{4} + \theta\right) \cdot \tan\left(\frac{3\pi}{4} + \theta\right)$

✳ Step 1: Use identity

$\tan\left(A + B\right) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$ But we don’t need expansion — use known angle values:

$\tan\left(\frac{\pi}{4} + \theta\right) = \frac{1 + \tan\theta}{1 - \tan\theta}$

$\tan\left(\frac{3\pi}{4} + \theta\right) = \frac{-1 + \tan\theta}{1 + \tan\theta}$

✳ Step 2: Multiply

$\left(\frac{1 + \tan\theta}{1 - \tan\theta}\right) \cdot \left(\frac{-1 + \tan\theta}{1 + \tan\theta}\right)$

Simplify:

$= \frac{(1 + \tan\theta)(-1 + \tan\theta)}{(1 - \tan\theta)(1 + \tan\theta)} = \frac{(\tan^2\theta - 1)}{1 - \tan^2\theta} = \boxed{-1}$

✅ Final Answer:

$\boxed{-1}$

Qus : 11

$\sin x=\sin y$ and

$\cos x=\cos y$ , then the value of x-y is

1
2
3
4
Go to Discussion

Solution

Given:

$\sin x = \sin y \quad \text{and} \quad \cos x = \cos y$

✳ Step 1: Use the identity for sine

$\sin x = \sin y \Rightarrow x = y + 2n\pi \quad \text{or} \quad x = \pi - y + 2n\pi$

✳ Step 2: Use the identity for cosine

$\cos x = \cos y \Rightarrow x = y + 2m\pi \quad \text{or} \quad x = -y + 2m\pi$

? Combine both conditions

For both $\sin x = \sin y$ and $\cos x = \cos y$ to be true, the only consistent solution is:

$x = y + 2n\pi \Rightarrow x - y = 2n\pi$

✅ Final Answer:

$\boxed{x - y = 2n\pi \quad \text{for } n \in \mathbb{Z}}$

Qus : 12

$a_1, a_2, a_3,...a_n$ , are in Arithmetic Progression with common difference d, then the sum

$(sind) (cosec a_1 . cosec a_2+cosec a_2.cosec a_2+...+cosec a_{n-1}.cosec a_n)$ is equal to

1
2
3
4
Go to Discussion

Solution

Qus : 13

In a ΔABC, if

$\tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k$ , then k is always

1
2
3
4
Go to Discussion

Solution

Qus : 14

The general value of

$\theta$ , satisfying the equation

$\sin \theta=\frac{-1}{2},\, \tan \theta=\frac{1}{\sqrt[]{3}}$

1
2
3
4
Go to Discussion

Solution

Qus : 15

then the value of

1
2
3
4
Go to Discussion

Solution

Qus : 16

If tan x = - 3/4 and 3π/2 < x < 2π, then the value of sin2x is

1
2
3
4
Go to Discussion

Solution

Qus : 17

The value of

$\tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}}$ is equal to

1
2
3
4
Go to Discussion

Solution

Qus : 18

If cosθ = 4/5 and cosϕ = 12/13, θ and ϕ both in the fourth quadrant, the value of cos( θ + ϕ )is

1
2
3
4
Go to Discussion

Solution

Qus : 19

The value of sin36^o is

1
2
3
4
Go to Discussion

Solution

Qus : 20

Express (cos 5x – cos7x) as a product of sines or cosines or sines and cosines,

1
2
3
4
Go to Discussion

Solution

Qus : 21

$32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha$ and

$3\, \cos \, 2\theta=1$ , then the general value of

$\alpha$ =

1
2
3
4
Go to Discussion

Solution

Qus : 22

If |k|=5 and 0° ≤ θ ≤ 360°, then the number of distinct solutions of 3cos⁡θ + 4sin⁡θ = k is

NIMCET 2021

1
2
3
4
Go to Discussion

Solution

Qus : 23

, then value of

1
2
3
4
Go to Discussion

Solution

Qus : 24

$a\, \cos \theta+b\, \sin \, \theta=2$ and

$a\, \sin \, \theta-b\, \cos \, \theta=3$ , then

${a}^{2^{}}+{b}^2=$

1
2
3
4
Go to Discussion

Solution

Qus : 25

The value of tan 1° tan 2° tan 3° ... tan 89° is:

1
2
3
4
Go to Discussion

Solution

Qus : 26

$P=sin^{20} \theta + cos^{48} \theta$ then the inequality that holds for all values of is

1
2
3
4
Go to Discussion

Solution

Qus : 27

$sin x + a cos x = b$ , then

$|a sin x - cos x|$ is:

1
2
3
4
Go to Discussion

Solution

Qus : 28

$0 < x < \pi$ and

$cos x + sin x = \frac{1}{2}$ , then the value of tan x is

1
2
3
4
Go to Discussion

Solution

Qus : 29

If tan A - tan B = x and cot B - cot A = y, then cot (A - B) is equal to

1
2
3
4
Go to Discussion

Solution

Qus : 30

The value of sin 20° sin 40° sin 80° is

1
2
3
4
Go to Discussion

Solution

Qus : 31

In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is