AP EAMCET · Maths · Trigonometric Equations
The number of solutions of the equation \(4 \cos 2 \theta \cos 3 \theta=\sec \theta\) in the interval \([0,2 \pi]\) is
- A \(12\)
- B \(8\)
- C \(16\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(12\)
Step-by-step Solution
Detailed explanation
\(4 \cos 2 \theta \cos 3 \theta \cos \theta = 1\), \(\cos \theta \neq 0\) \(2 \cos 2 \theta (\cos 4 \theta + \cos 2 \theta) = 1\) \(\cos 6 \theta + \cos 4 \theta + \cos 2 \theta = 0\) \(\cos 4 \theta (2 \cos 2 \theta + 1) = 0\) If \(\cos 4 \theta = 0\):…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are need isAP EAMCET 2012 Easy
- \(\mathrm{P}(\mathrm{A} / \mathrm{A} \cap \mathrm{B})+\mathrm{P}(\mathrm{B} / \mathrm{A} \cap \mathrm{B})=\)AP EAMCET 2024 Easy
- If \((1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}, \quad\) then \(\sum_{r=1}^{15} r \frac{a_r}{a_r-1}\) is equal toAP EAMCET 2005 Hard
- If a normal chord at a point \(t(\neq 0)\) on the parabola \(y^2=9 x\) subtends a right angle at its vertex, then \(t=\)AP EAMCET 2019 Medium
- If the equation of the base of an equilateral triangle is \(x+y=6\) and the opposite vertex is the point \((-1,-1)\) then the area of the triangle is equal to sq. unitsAP EAMCET 2020 Easy
- If \(\left|\frac{x^2+k x+1}{x^2+x+1}\right| < 3\) for all real numbers \(x\), then the range of the parameter \(k\) isAP EAMCET 2019 Easy
More PYQs from AP EAMCET
- The ratio of radii of \(3^{\text {rd }}\) and \(6^{\text {th }}\) Bohr's orbit in a hydrogen atom isAP EAMCET 2022 Medium
- Two concentric coplanar circular conducting loops have radii \(R\) and \(r(R \gg r)\). Their mutual inductance is proportional toAP EAMCET 2019 Easy
- \(\{x \in R:[x-|x|]=5\}\) is equal toAP EAMCET 2005 Easy
- \(\lim _{x \rightarrow 0} \frac{x^2 \sin ^2(3 x)+\sin ^4(6 x)}{(1-\cos 3 x)^2}=\)AP EAMCET 2025 Medium
- If \(2 x^2-3 x y+y^2=0\) represents two sides of a triangle and \(x+y-1=0\) is its third side, then the distance between the orthocenter and the circumcentre of that triangle isAP EAMCET 2023 Medium
- \(\int_0^{\pi / 2} \frac{1}{1+\sqrt{\tan x}} d x=\)AP EAMCET 2024 Medium