JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(\frac{\cos ^2 48^{\circ}-\sin ^2 12^{\circ}}{\sin ^2 24^{\circ}-\sin ^2 6^{\circ}}=\frac{\alpha+\beta \sqrt{5}}{2}\), where \(\alpha, \beta \in N\), then \(\alpha+\beta\) is equal to ___ .
- A 2
- B 4
- C 6
- D 8
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
Use \(\sin ( A + B ) \sin ( A + B )=\sin ^2 A-\sin ^2 B\) \(\cos (A+B) \cos (A-B)=\cos ^2 A-\sin ^2 B\)…
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
- In the expansion of \((1+x)\left(1-x^2\right)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5, x \neq 0\), the sum of the coefficient of \(x^3\) and \(x^{-13}\) is equal toJEE Mains 2024 Hard
- The angle of elevation of a jet plane from a point \(A\) on the ground is \(60^{\circ}\). After a flight of \(20\, seconds\) at the speed of \(432\, km / hour\), the angle of elevation changes to \(30^{\circ}\). If the jet plane is flying at a constant height, then its height is ..... \(m.\)JEE Mains 2021 Hard
- Let \(A=\{1,2,3,4,5\}\) and \(B=\{1,2,3,4,5,6\}\). Then the number of functions \(f: A \rightarrow B\) satisfying \(f(1)+f(2)=f(4)-1\) is equal toJEE Mains 2023 Hard
- Let a line \(l\) pass through the origin and be perpendicular to the lines \(l_1: \overrightarrow{ r }=(\hat{ i }-11 \hat{ j }-7 \hat{ k })+\lambda(\hat{ i }+2 \hat{ j }+3 \hat{ k }), \lambda \in R\) and \(l_2: \overrightarrow{ r }=(-\hat{ i }+\hat{ k })+\mu(2 \hat{ i }+2 \hat{ j }+\hat{ k }), \mu \in R\). If \(P\) is the point of intersection of \(l\) and \(l_1\), and \(Q (\alpha\) \(, \beta, \gamma)\) is the foot of perpendicular from \(P\) on \(l_2\), then \(9(\alpha+\beta+\gamma)\) is equal to \(..........\).JEE Mains 2023 Hard
- Let the foot of perpendicular from the point \(A (4,3\), 1) on the plane \(P: x-y+2 z+3=0\) be N. If \(B(5\), \(\alpha, \beta), \alpha, \beta \in Z\) is a point on plane \(P\) such that the area of the triangle \(A B N\) in \(3 \sqrt{2}\), then \(\alpha^2+\beta^2+\alpha \beta\) is equal to \(...........\).JEE Mains 2023 Hard
- The system of equations \(-k x+3 y-14 z=25\) \(-15 x+4 y-k z=3\) \(-4 x+y+3 z=4\) is consistent for all \(k\) in the setJEE Mains 2022 Medium
More PYQs from JEE Mains
- Two poles, \(\mathrm{AB}\) of length \(a\) metres and \(\mathrm{CD}\) of length \(\mathrm{a}+\mathrm{b}(\mathrm{b} \neq \mathrm{a})\) metres are erected at the same horizontal level with bases at \(\mathrm{B}\) and \(\mathrm{D} .\) If \(\mathrm{BD}=\mathrm{x}\) and \(\tan \angle\,ACB=\frac{1}{2}\), then:JEE Mains 2021 Hard
- The normal to the curve \(y\left( {x - 2} \right)\left( {x - 3} \right) = x + 6\) at the point where the curve intersects the \(y - \)axis passes through the point :JEE Mains 2017 Medium
- A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of \(4\). Then the conditional probability that the score \(4\) has appeared at least once isJEE Mains 2020 Medium
- Let a line \(L_{1}\) be tangent to the hyperbola \(\frac{x^{2}}{16}-\frac{y^{2}}{4}=1\) and let \(L_{2}\) be the line passing through the origin and perpendicular to \(L _{1}\). If the locus of the point of intersection of \(L_{1}\) and \(L_{2}\) is \(\left(x^{2}+y^{2}\right)^{2}=\) \(\alpha x^{2}+\beta y^{2}\), then \(\alpha+\beta\) is equal toJEE Mains 2022 Hard
- Let \(\vec u\;\)be a vector coplanar with the vector \(\vec a = 2\hat i + 3\hat j - \hat k\) and \(\vec b = \hat j + \hat k\) . If \(\vec u\) is perpendicular to \(\vec a\) and \(\vec u \cdot \vec b = 24\) ,then \({\left| {\vec u} \right|^2} = \) . . . .JEE Mains 2018 Hard
- Let the equation of two diameters of a circle \(x ^{2}+ y ^{2}\) \(-2 x +2 fy +1=0\) be \(2 px - y =1\) and \(2 x + py =4 p\). Then the slope \(m \in(0, \infty)\) of the tangent to the hyperbola \(3 x^{2}-y^{2}=3\) passing through the centre of the circle is equal to \(......\)JEE Mains 2022 Hard