Trigonometric Functions & Identities Questions with Solutions

47 questions16 easy24 medium7 hard

Trigonometric functions (sine, cosine, tangent and their reciprocals) relate the angles of a right triangle to the ratios of its sides, and extend to any angle using the unit circle. This topic covers degree and radian measure, values of trigonometric ratios at standard angles, signs in the four quadrants, and allied angles such as (90 - theta) and (180 + theta). It also covers the main identities: sin^2 + cos^2 = 1 and its variations, compound angle formulas such as sin(A + B), multiple and sub-multiple angle formulas such as sin 2A and cos 2A, and the sum-to-product and product-to-sum formulas. Most questions are about choosing the right identity to simplify an expression or prove an equality, so learning these formulas thoroughly pays off. Practise the trigonometric functions and identities questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
If $s in x + s in^{2} x = 1$ , then $cos^{2} x + cos^{4} x$ is equal to
A. 0B. 1C. -1D. 2
easyAsked in NIMCET 2013View solution ›
Q2.
If $s in^{2} x = 1 - s in x$ , then $cos^{4} x + cos^{2} x$ is equal to
A. 0B. 1C. $\frac{2}{3}$ D. -1
easyAsked in NIMCET 2012View solution ›
Q3.
If $A - B = \frac{π}{4}$ , then $(1 + t an A) (1 - t an B)$ is equal to
A. 2B. 1C. 0D. 3
easyAsked in NIMCET 2012View solution ›
Q4.
Which of the following is correct?
A. $s in 1^{\circ} > s in 1$ B. $s in 1^{\circ} < s in 1$ C. $s in 1^{\circ} = s in 1$ D. $s in 1^{\circ} = \frac{π}{180} s in 1$
easyAsked in NIMCET 2012View solution ›
Q5.
The value of $s in 30^{\circ} cos 45^{\circ} + cos 30^{\circ} s in 45^{\circ}$ is
A. $\frac{1 - 3}{2}$ B. $\frac{3 + 1}{2 2}$ C. $\frac{2}{3}$ D. $\frac{3}{2}$
easyAsked in NIMCET 2011View solution ›
Q6.
The value of $\frac{1 - t an ^{2} 15 ^{\circ}}{1 + t an ^{2} 15 ^{\circ}}$ is
A. $1$ B. $3$ C. $\frac{3}{2}$ D. $2$
easyAsked in NIMCET 2011View solution ›
Q7.
If $A = cos^{2} θ + s in^{4} θ$ , then for all values of $θ$ :
A. $1 \leq A \leq 2$ B. $\frac{13}{16} \leq A \leq 1$ C. $\frac{3}{4} \leq A \leq \frac{13}{16}$ D. $\frac{3}{4} \leq A \leq 1$
easyAsked in NIMCET 2009View solution ›
Q8.
The value of $s in 10^{\circ} s in 50^{\circ} s in 70^{\circ}$ is
A. $\frac{1}{4}$ B. $\frac{1}{2}$ C. $\frac{3}{4}$ D. $\frac{1}{8}$
easyAsked in NIMCET 2020View solution ›
Q9.
If $a cos θ + b s in θ = 2$ and $a s in θ - b cos θ = 3$ , then $a^{2} + b^{2} =$
A. 6B. 5C. 13D. 10
easyAsked in NIMCET 2021View solution ›
Q10.
If $cosec θ - co tθ = 2$ , then the value of $cosec θ$ is
A. $\frac{5}{2}$ B. $\frac{3}{5}$ C. $\frac{4}{5}$ D. $\frac{5}{4}$
easyAsked in NIMCET 2022View solution ›
Q11.
The value of $t an 1^{\circ} t an 2^{\circ} t an 3^{\circ} \dots t an 89^{\circ}$ is:
A. $0$ B. $\frac{1}{2}$ C. $1$ D. $2$
easyAsked in NIMCET 2014View solution ›
Q12.
The value of $t an (\frac{7 π}{8})$ is
A. $1 - 2$ B. $1 + 2$ C. $2 + 3$ D. $2 - 3$
easyAsked in NIMCET 2015View solution ›
Q13.
If $t an x = - \frac{3}{4}$ and $\frac{3 π}{2} < x < 2 π$ , then the value of $s in 2 x$ is
A. $\frac{7}{25}$ B. $- \frac{7}{25}$ C. $\frac{24}{25}$ D. $- \frac{24}{25}$
easyAsked in NIMCET 2017View solution ›
Q14.
If $cos θ = \frac{4}{5}$ and $cos ϕ = \frac{12}{13}$ , $θ$ and $ϕ$ both in the fourth quadrant, the value of $cos (θ + ϕ)$ is
A. $- \frac{16}{65}$ B. $- \frac{33}{65}$ C. $\frac{33}{65}$ D. $\frac{16}{65}$
easyAsked in NIMCET 2017View solution ›
Q15.
Express $(cos 5 x - cos 7 x)$ as a product of sines or cosines or sines and cosines.
A. $2 cos 4 x cos x$ B. $2 s in 4 x s in x$ C. $2 s in 6 x s in x$ D. $2 cos 6 x cos x$
easyAsked in NIMCET 2017View solution ›
Q16.
The maximum value of $s in x + s in (x + 1)$ is $k cos \frac{1}{2}$ . Then the value of $k$ is
A. 1B. 2C. 3D. None of these
easyAsked in NIMCET 2025View solution ›