Trigonometric Ratios and Identities — JEE Main PYQs

68 previous year questions on Trigonometric Ratios and Identities (Mathematics), newest first. Open any question for its complete step-by-step solution.

If $cos (α + β) = \frac{3}{5}, sin (α - β) = \frac{5}{13}$ and $0 < α, β < \frac{π}{4}$ , then $tan (2 α)$ is equal to:
JEE Main 2019View solution →
The value of $cos^{2} 1 0^{\circ} - cos 1 0^{\circ} cos 5 0^{\circ} + cos^{2} 5 0^{\circ}$ is:
JEE Main 2019View solution →
The equation $y = sin x sin (x + 2) - sin^{2} (x + 1)$ represents a straight line lying in :
JEE Main 2019View solution →
Let $f_{k} (x) = \frac{1}{k} (sin^{k} x + cos^{k} x)$ for $k = 1, 2, 3, \dots$ Then for all $x \in R$ , the value of $f_{4} (x) - f_{6} (x)$ is equal to:
JEE Main 2019View solution →
The maximum value of $3 cos θ + 5 sin (θ - \frac{π}{6})$ for any real value of $θ$ is:
JEE Main 2019View solution →
If $sin^{4} α + 4 cos^{4} β + 2 = 42 sin α cos β$ ; $α, β \in [0, π]$ , then $cos (α + β) - cos (α - β)$ is equal to :
JEE Main 2019View solution →
The value of $sin 1 0^{\circ} sin 3 0^{\circ} sin 5 0^{\circ} sin 7 0^{\circ}$ is
JEE Main 2019View solution →
For any $θ \in (\frac{π}{4}, \frac{π}{2})$ , the expression $3 (sin θ - cos θ)^{4} + 6 (sin θ + cos θ)^{2} + 4 sin^{6} θ$ equals:
JEE Main 2019View solution →
All the pairs $(x, y)$ that satisfy the inequality
$2^{s i n^{2} x - 2 s i n x + 5} \cdot \frac{1}{4 ^{s i n^{2} y}} \leq 1$ also
satisfy the equation:
JEE Main 2019View solution →
If $5 (tan^{2} x - cos^{2} x) = 2 cos 2 x + 9$ , then the value of $cos 4 x$ is :
JEE Main 2017View solution →
Let $f_{K} (x) = \frac{1}{k} (sin^{k} x + cos^{k} x)$ where $x \in R$ and $k \geq 1$ . Then $f_{4} (x) - f_{6} (x)$ equals
JEE Main 2014View solution →
The expression $\frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A}$ can be written as
JEE Main 2013View solution →
If $A = sin^{2} x + cos^{4} x$ , then for all real x
JEE Main 2011View solution →
Let $cos (α + β) = \frac{4}{5}$ and let $sin (α - β) = \frac{5}{13}$ , where $0 \leq α, β \leq \frac{π}{4}$ , then $tan 2 α =$
JEE Main 2010View solution →
For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is
JEE Main 2010View solution →
Let $A$ and $B$ denote the statements
A: $cos α + cos β + cos γ = 0$
B: $sin α + sin β + sin γ = 0$
If $cos (β - γ) + cos (γ - α) + cos (α - β) = - \frac{3}{2}$ , then
JEE Main 2009View solution →
If $0 < x < π$ and $cos x + sin x = \frac{1}{2}$ , then $tan x$ is
JEE Main 2006View solution →
Let $α, β$ be such that $π < α - β < 3 π$ . If $sin α + sin β = - \frac{21}{65}$ and $cos α + cos β = - \frac{27}{65}$ , then the value of $cos \frac{α - β}{2}$ is
JEE Main 2004View solution →