JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9,\) then \(\cos 4x\) is equal to
- A \( - \frac{7}{9}\)
- B \( - \frac{3}{5}\)
- C \(\frac{1}{3}\)
- D \(\frac{2}{9}\)
Answer & Solution
Correct Answer
(A) \( - \frac{7}{9}\)
Step-by-step Solution
Detailed explanation
We have \(5\,{\tan ^2}x\, - 5{\cos ^2}x = 2(2{\cos ^2}x - 1) + 9\) \( \Rightarrow \,5\,{\tan ^2}x\, - 5{\cos ^2}x = 4{\cos ^2}x - 2 + 9\) \( \Rightarrow \,5\,{\tan ^2}x = 9{\cos ^2}x + 7\) \( \Rightarrow \,5\,({\sec ^2}x - 1) = 9{\cos ^2}x + 7\) Let \({\cos ^2}x = t\)…
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 the system of linear equations \(-x+2 y-9 z=7\) \(-x+3 y+7 z=9\) \(-2 x+y+5 z=8\) \(-3 x+y+13 z=\lambda\) has a unique solution \(x =\alpha, y =\beta, z =\gamma\). Then the distance of the point \((\alpha, \beta, \gamma)\) from the plane \(2 x-2 y+z=\lambda\) isJEE Mains 2023 Hard
- The smallest natural number \(n,\) such that the coefficient of \(x\) in the expansion of \({\left( {{x^2}\, + \,\frac{1}{{{x^3}}}} \right)^n}\) is \(^n{C_{23}}\) isJEE Mains 2019 Hard
- The number of words, with or without meaning, that can be formed using all the letters of the word \(ASSASSINATION\) so that the vowels occur together, is \(.............\).JEE Mains 2023 Hard
- The coefficient of \(x^{18}\) in the expansion of \(\left(x^4-\frac{1}{x^3}\right)^{15}\) is \(...........\).JEE Mains 2023 Hard
- If the quadratic equation \((\lambda+2)x^2-3\lambda x+4\lambda=0\), \(\lambda \neq -2\), has two positive roots, then the number of possible integral values of \(\lambda\) is:JEE Mains 2026 Medium
- Let the domains of the functions
\(\mathrm{f}(\mathrm{x})=\log _4 \log _3 \log _7\left(8-\log _2\left(\mathrm{x}^2+4 \mathrm{x}+5\right)\right)\) and \(g(x)=\sin ^{-1}\left(\frac{7 x+10}{x-2}\right)\) be \((\alpha, \beta)\) and \([\gamma, \delta]\), respectively. Then \(\alpha^2+\beta^2+\gamma^2+\delta^2\) is equal to :-JEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \(A=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix, where \(a_{i j}= 1 , \quad\quad\text { if } i=j\) \(\quad\quad-x ,\quad \text { if }|i-j|=1\) \(\quad\quad2 x+1, \text { otherwise }\) Let a function f: \(\mathrm{R} \rightarrow \mathrm{R}\) be defined as \(\mathrm{f}(\mathrm{x})=\operatorname{det}(\mathrm{A})\). Then the sum of maximum and minimum values of \(f\) on \(R\) is equal to:JEE Mains 2021 Medium
- If \(\displaystyle\sum_{k=1}^{n} a_k = 6n^3\), then \(\displaystyle\sum_{k=1}^{6} \left(\dfrac{a_{k+1} - a_k}{36}\right)^2\) is equal to _______.JEE Mains 2026 Medium
- If \(f\left( x \right) = {\log _e}\,\left( {\frac{{1 - x}}{{1 + x}}} \right)\), \(\left| x \right| < 1\), then \(f\left( {\frac{{2x}}{{1 + {x^2}}}} \right)\) is equal toJEE Mains 2019 Hard
- Let \(y = y(x)\) be the solution of the differential equation \((x^2 - x\sqrt{x^2 - 1})dy + (y(x - \sqrt{x^2 - 1}) - x)dx = 0\), \(x \geq 1\). If \(y(1) = 1\), then the greatest integer less than \(y(\sqrt{5})\) is _______.JEE Mains 2026 Hard
- Let \(x=2\) be a local minima of the function \(f(x)=2 x^4-18 x^2+8 x+12, x \in(-4,4)\). If \(M\) is local maximum value of the function \(f\) in \((-4,4)\), then \(M =\)JEE Mains 2023 Hard
- The curve \(y(x)=a x^{3}+b x^{2}+c x+5\) touches the \(x\)-axis at the point \(P (-2,0)\) and cuts the \(y\)-axis at the point \(Q\), where \(y ^{\prime}\) is equal to \(3\) . Then the local maximum value of \(y ( x )\) is.JEE Mains 2022 Hard