Trigonometric Ratios and Identities — JEE Advanced PYQs

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

Let
$α = \frac{1}{sin 6 0 ^{\circ} sin 6 1 ^{\circ}} + \frac{1}{sin 6 2 ^{\circ} sin 6 3 ^{\circ}} + \dots + \frac{1}{sin 11 8 ^{\circ} sin 11 9 ^{\circ}} .$

Then the value of
$(\frac{cosec 1 ^{o}}{α})^{2}$

is ____.
JEE Advanced 2025View solution →
Let $\frac{π}{2} < x < π$ be such that $cot x = \frac{- 5}{11}$ . Then
$(sin \frac{11 x}{2}) (sin 6 x - cos 6 x) + (cos \frac{11 x}{2}) (sin 6 x + cos 6 x)$ is equal to :
JEE Advanced 2024View solution →
Let $α$ and $β$ be real numbers such that $- \frac{π}{4} < β < 0 < α < \frac{π}{4}$ . If $sin (α + β) = \frac{1}{3}$ and $cos (α - β) = \frac{2}{3}$ , then the greatest integer less than or equal to …
JEE Advanced 2022View solution →
For non-negative integers n, let
$f (n) = \frac{\sum _{k = 0}^{n} sin ( \frac{k + 1}{n + 2} π ) sin ( \frac{k + 2}{n + 2} π )}{\sum _{k = 0}^{n} sin ^{2} ( \frac{k + 1}{n + 2} π )}$

Assuming $cos^{- 1} x$ takes values in $[0, π]$ , which of the foll …
JEE Advanced 2019View solution →
The value of $sec^{- 1} (\frac{1}{4} \sum_{k = 0}^{10} sec (\frac{7 π}{12} + \frac{k π}{2}) sec (\frac{7 π}{12} + \frac{( k + 1 ) π}{2}))$ in the interval $[- \frac{π}{4}, \frac{3 π}{4}]$ equals
JEE Advanced 2019View solution →
Let $α$ and $β$ be nonzero real numbers such that $2 (cos β - cos α) + cos α cos β = 1$ . Then which of the following is/are true?
JEE Advanced 2017View solution →
Let $O$ be the origin, and $O X, O Y, O Z$ be three unit vectors in the directions of the sides $QR, R P, P Q$ , respectively, of a triangle $P QR$ .

If the triangle $P QR$ varie …
JEE Advanced 2017View solution →
Match List-I with List-II and select the correct answer using the code given below the lists :
List-I List-II
| P. | …
JEE Advanced 2013View solution →
Let $f : (- 1, 1) \to R$ be such that $f (cos 4 θ) = \frac{2}{2 - s e c ^{2} θ}$ for $θ \in (0, \frac{π}{4}) \cup (\frac{π}{4}, \frac{π}{2})$ . Then the value(s) of $f (\frac{1}{3})$ is (are)
JEE Advanced 2012View solution →
The maximum value of the expression $\frac{1}{s i n ^{2} θ + 3 s i n θ c o s θ + 5 c o s ^{2} θ}$ is
JEE Advanced 2010View solution →
For $0 < θ < \frac{π}{2}$ , the solution(s) of
$m = 1 \sum 6 cosec (θ + \frac{( m - 1 ) π}{4}) cosec (θ + \frac{mπ}{4}) = 42$

is(are)
JEE Advanced 2009View solution →
If
$\frac{sin ^{4} x}{2} + \frac{cos ^{4} x}{3} = \frac{1}{5},$

then
JEE Advanced 2009View solution →