NIMCET Trigonometry Previous Year Question Paper and Solution with PDF

Solution

Qus : 9NIMCET PYQ

If $sin x + a cos x = b$, then what is the expression for $|a sin x – cos x|$ in terms of $a$ and $b$?

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Solution

Qus : 10NIMCET PYQ

The value of $\tan\theta+2\tan2\theta + 4\tan4\theta + 8\cot8\theta$ is

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Solution

Qus : 11NIMCET PYQ

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

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Solution

Given $\,\csc\theta-\cot\theta=2\,$ and the identity $\;(\csc\theta-\cot\theta)(\csc\theta+\cot\theta)=1\;$, we get $$\csc\theta+\cot\theta=\frac{1}{2}.$$ Adding the two equations: $$(\csc\theta-\cot\theta)+(\csc\theta+\cot\theta) $$ $$=2+\frac{1}{2}$$ $$\;\Rightarrow\;2\,\csc\theta=\frac{5}{2}.$$ Hence $$\csc\theta=\frac{5}{4}.$$

Qus : 12NIMCET PYQ

The solution of the equation ${4\cos }^2x+6{\sin }^2x=5$ are

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Solution

Qus : 13NIMCET PYQ

If $\sin x + \sin^{2}x = 1$, then $\cos^{2}x + \cos^{4}x$ is equal to.

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Solution

Qus : 14NIMCET PYQ

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

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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 : 15NIMCET PYQ

If $tan\alpha=\frac{m}{m+1}$ and $tan\beta=\frac{1}{2m+1}$ then $\alpha+\beta$ is equal to

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Solution

Qus : 16NIMCET PYQ

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

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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 : 17NIMCET PYQ

If $a_1, a_2, a_3,...a_n$, 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

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Solution

Qus : 18NIMCET PYQ

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

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Solution

Qus : 19NIMCET PYQ

The general value of $\theta$, satisfying the equation $\sin \theta=\frac{-1}{2},\, \tan \theta=\frac{1}{\sqrt[]{3}}$

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Solution

Qus : 20NIMCET PYQ

then the value of

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Solution

Qus : 21NIMCET PYQ

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

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Solution

Qus : 22NIMCET PYQ

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

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Solution

Qus : 23NIMCET PYQ

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

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Solution

Qus : 24NIMCET PYQ

The value of sin36^o is

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Solution

Qus : 25NIMCET PYQ

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

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Solution

Qus : 26NIMCET PYQ

If $32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha$ and $3\, \cos \, 2\theta=1$, then the general value of $\alpha$ =

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Solution

Qus : 27NIMCET PYQ

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

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Solution

Qus : 28NIMCET PYQ

If $B=sin^2 y+cos^4 y$, then for all real y

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Solution

Qus : 29NIMCET PYQ

The maximum value of $sinx+sin(x+1)$ is $k cos \frac{1}{2}$. Then the value of k is

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Solution

Qus : 30NIMCET PYQ

, then value of

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Solution

Qus : 31NIMCET PYQ

What is the general solution of the equation $tan \theta + cot \theta = 2$ ?

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Solution

Qus : 32NIMCET PYQ

If $a\, \cos \theta+b\, \sin \, \theta=2$ and $a\, \sin \, \theta-b\, \cos \, \theta=3$ , then ${a}^{2^{}}+{b}^2=$

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Solution

Qus : 33NIMCET PYQ

If $cos^2(10°)cos(20°)cos(40°)cos(50°) cos(70°) = \alpha+\frac{\sqrt{3}}{16} cos(10°)$, then $3\alpha^{-1}$ is equal to

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Solution

Qus : 34NIMCET PYQ

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

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Solution

Qus : 35NIMCET PYQ

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

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Solution

Qus : 36NIMCET PYQ

If $sin x + a cos x = b$, then $|a sin x - cos x|$ is:

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Solution

Qus : 37NIMCET PYQ

If $0 < x < \pi $ and $cos x + sin x = \frac{1}{2}$ , then the value of tan x is

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Solution

Qus : 38NIMCET PYQ

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

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Solution

Qus : 39NIMCET PYQ

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

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