JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If for \(x \in\left(0, \frac{\pi}{2}\right), \log _{10} \sin x+\log _{10} \cos x=-1\) and \(\log _{10}(\sin x+\cos x)=\frac{1}{2}\left(\log _{10} n-1\right), n>0\) then the value of \(n\) is equal to
- A \(20\)
- B \(12\)
- C \(9\)
- D \(16\)
Answer & Solution
Correct Answer
(B) \(12\)
Step-by-step Solution
Detailed explanation
\(x \in\left(0, \frac{\pi}{2}\right)\) \(\log _{10} \sin x+\log _{10} \cos x=-1\) \(\Rightarrow \quad \log _{10} \sin x \cdot \cos x=-1\) \(\Rightarrow \quad \sin x \cdot \cos x=\frac{1}{10}\) \(....(1)\) \(\log _{10}(\sin x+\cos x)=\frac{1}{2}\left(\log _{10} n-1\right)\)…
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
- The area of the region \(\left\{(x, y): y^2 \leq 4 x, x<4, \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0, x \neq 3\right\}\) isJEE Mains 2024 Hard
- If \(a\) and \(b\) are real numbers such that \((2+\alpha)^{4}=a+b \alpha,\) where \(\alpha=\frac{-1+i \sqrt{3}}{2},\) then \(a+b\) is equal toJEE Mains 2020 Hard
- Consider function \(f: A \rightarrow B\) and \(g: B \rightarrow C(A, B, C \subseteq R)\) such that \((gof) ^{-1}\) exists, then:JEE Mains 2021 Medium
- If \(\vec{a} = \hat{i} + \hat{j} + \hat{k}\), \(\vec{b} = \hat{j} - \hat{k}\) and \(\vec{c}\) be three vectors such that \(\vec{a} \times \vec{c} = \vec{b}\) and \(\vec{a} \cdot \vec{c} = 3\), then \(\vec{c} \cdot (\vec{a} - 2\vec{b})\) is equal to _______.JEE Mains 2026 Medium
- Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability that the ball drawn is white is \( p/q \) (where \( gcd(p,q)=1 \)), then \( p+q \) is equal to:JEE Mains 2026 Easy
- Two vertical poles of heights, \(20\, m\) and \(80\,m\) stand a apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from his horizontal plane isJEE Mains 2019 Hard
More PYQs from JEE Mains
- The locus of a point, which moves such that the sum of squares of its distances from the points \((0,0),(1,0),(0,1)(1,1)\) is \(18\) units, is a circle of diameter \(\mathrm{d}\). Then \(\mathrm{d}^{2}\) is equal to ...... .JEE Mains 2021 Medium
- Let \(f(x) = log_e\,(sin\,x),\) \((0\,<\,x\,< \pi )\) and \(g(x) = sin^{-1}\,(e^{-x}),\) \((x\, \ge \,0)\). If \(\alpha \) is a positive real number such that \(a\) \( = (fog)’(\alpha )\) and \(b = (fog)(\alpha ),\) thenJEE Mains 2019 Hard
- The value of \((0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+\ldots . to \infty\right)}\) is equal toJEE Mains 2020 Hard
- A water tank has the shape of an inverted right circular cone, whose semi vertical angle is \({\tan ^{ - 1}}\,\left( {\frac{1}{2}} \right)\). Water is poured in at a constant rate of \(5\) cubic meter per minute. Then the rate (in \(m/min\)) at which the level of water is rising at the instant when the depth of water in the tank is \(10\, m\) isJEE Mains 2019 Hard
- Let \(S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\right.\) \(\left(\sin ^6 \theta+\cos ^6 \theta\right)=0\) has real roots\(\}\). If \(\alpha\) and \(\beta\) be the smallest and largest elements of the set \(S\), respectively, then \(3\left((\alpha-2)^2+(\beta-1)^2\right)\) equals ...........JEE Mains 2024 Hard
- Let \(\theta \in\left(0, \frac{\pi}{2}\right)\). If the system of linear equations \(\left(1+\cos ^{2} \theta\right) x+\sin ^{2} \theta y+4 \sin 3 \theta z=0\) \(\cos ^{2} \theta x+\left(1+\sin ^{2} \theta\right) y+4 \sin 3 \theta z=0\) \(\cos ^{2} \theta x+\sin ^{2} \theta y+(1+4 \sin 3 \theta) z=0\) has a non-trivial solution, then the value of \(\theta\) is :JEE Mains 2021 Hard