JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}\) satisfies the equation \(t ^{2}-9 t +8=0,\) then the value of \(\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)\) is
- A \(2 \sqrt{3}\)
- B \(\frac{3}{2}\)
- C \(\sqrt{3}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(e ^{\left(\cos ^{2} \theta+\cos ^{4} \theta+\ldots . . \infty\right) \ell n ^{2}}=2^{\cos ^{2} \theta+\cos ^{4} \theta+\ldots \infty}\) \(=2^{\cot ^{2} \theta}\) Now \(t^{2}-9 t+9=0 \Rightarrow t=1,8\)…
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
- Let \(f, g: R \rightarrow R\) be two real valued functions defined as \(f(x)=\left\{\begin{array}{cl}-|x+3| & , \quad x<0 \\ e^{x} & , \quad x \geq 0\end{array}\right.\) and \(g(x)=\left\{\begin{array}{ll}x^{2}+k_{1} x & , \quad x<0 \\ 4 x+k_{2} & , \quad x \geq 0\end{array}\right.\), where \(k_{1}\) and \(k_{2}\) are real constants. If \((gof)\) is differentiable at \(x=0\), then \((gof) (-4)+(gof)\, (4)\) is equal toJEE Mains 2022 Hard
- Let \(\omega=z \bar{z}+k_1 z+k_2 i z+\lambda(1+i), k_1, k_2 \in R\). Let \(\operatorname{Re}(\omega)=0\) be the circle \(C\) of radius 1 in the first quadrant touching the line \(y=1\) and the \(y\)-axis. If the curve \(\operatorname{Im}(\omega)=0\) intersects \(C\) at \(A\) and \(B\), then \(30(A B)^2\) is equal to \(.......\).JEE Mains 2023 Hard
- If the coefficents of \({x^3}\) and \({x^4}\) in the expansion of \(\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}\) in powers of \(x\) are both zero, then \( (a,b) \) is equal toJEE Mains 2014 Hard
- If \(\left| {\begin{array}{*{20}{c}}{x - 4}&{2x}&{2x}\\{2x}&{x - 4}&{2x}\\{2x}&{2x}&{x - 4}\end{array}} \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2},\) then the ordered pair \(\left( {A,B} \right) = \). . . . .JEE Mains 2018 Medium
- If the length of the latus rectum of a parabola, whose focus is \(( a , a )\) and the tangent at its vertex is \(x+y=a\), is \(16 \), then \(|a|\) is equal to.JEE Mains 2022 Medium
- The interior angles of a polygon with n sides, are in an A.P. with common difference \(6^{\circ}\). If the largest interior angle of the polygon is \(219^{\circ}\), then n is equal toJEE Mains 2025 Easy
More PYQs from JEE Mains
- Bag \(A\) contains \(3\) white, \(7\) red balls and bag \(B\) contains \(3\) white, \(2\) red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag \(\mathrm{A}\), if the ball drawn in white, is :JEE Mains 2024 Medium
- If the number of words, with or without meaning, which can be made using all the letters of the word \(MATHEMATICS\) in which \(C\) and \(S\) do not come together, is \((6 !) k\), then \(k\) is equal to \(............\).JEE Mains 2023 Hard
- Let \(P (a, b )\) be a point on the parabola \(y ^{2}=8 x\) such that the tangent at \(P\) passes through the centre of the circle \(x ^{2}+ y ^{2}-10 x -14 y +65=0\). Let \(A\) be the product of all possible values of \(a\) and \(B\) be the product of all possible values of \(b\). Then the value of \(A + B\) is equal to.JEE Mains 2022 Hard
- The value of \( \frac{^{100}C_{50}}{51} + \frac{^{100}C_{51}}{52} + \dots + \frac{^{100}C_{100}}{101} \) is:JEE Mains 2026 Medium
- With the usual notation, in \(\Delta ABC\), if \(\angle A + \angle B = {120^o}\), \(a = \sqrt 3 - 1\), then the ratio \(\angle A : \angle B\), isJEE Mains 2019 Hard
- The sum of the infinite series \(1+\frac{2}{3}+\frac{7}{3^{2}}+\frac{12}{3^{3}}+\frac{17}{3^{4}}+\frac{22}{3^{5}}+\ldots\) is equal toJEE Mains 2021 Hard