MHT CET · Maths · Trigonometric Ratios & Identities
If \(\cos x+\cos y=-\cos \alpha, \sin x+\sin y=-\sin \alpha\), then \(\cot \left(\frac{x+y}{2}\right)=\)
- A \(-\cot \propto\)
- B \(\cot \propto\)
- C \(-\tan \propto\)
- D \(\tan \propto\)
Answer & Solution
Correct Answer
(B) \(\cot \propto\)
Step-by-step Solution
Detailed explanation
Given \(\cos x+\cos y=-\cos \alpha\) and \(\sin x+\sin y=-\sin \alpha\)
\(2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\cos \alpha\) ...(1) and
\(2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\sin \alpha\) ...(2)
Divided equation (1) by equation (2)
\(\cot \left(\frac{x+y}{2}\right)=\cot \alpha\)
\(2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\cos \alpha\) ...(1) and
\(2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\sin \alpha\) ...(2)
Divided equation (1) by equation (2)
\(\cot \left(\frac{x+y}{2}\right)=\cot \alpha\)
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 number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, isMHT CET 2025 Medium
- If the angles \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) of a triangle are in an Arithmetic Progression and if \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression \(\frac{\mathrm{a}}{\mathrm{c}} \sin 2 \mathrm{C}+\frac{\mathrm{c}}{\mathrm{a}} \sin 2 \mathrm{~A}\) isMHT CET 2023 Medium
- Suppose that \(\bar{p}, \bar{q}\) and \(\bar{r}\) are three non-coplanar vectors in \(\mathbb{R}^3\). Let the components of a vector \(\bar{s}\) along \(\bar{p}, \bar{q}\) and \(\bar{r}\) be 4,3 and 5 respectively. If the components of this vector \(\overline{\mathrm{s}}\) along \((-\overline{\mathrm{p}}+\overline{\mathrm{q}}+\overline{\mathrm{r}}),(\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})\) and \((-\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})\) are \(x\), \(y\) and \(z\) respectively, then the value of \(2 x+y+z\) isMHT CET 2024 Medium
- If \(|z|=1\) and \(w=\frac{z-1}{z+1}\) (where \(z \neq-1\) ), then \(\operatorname{Re}(\mathrm{w})\) isMHT CET 2024 Medium
- If \(y=\tan ^{-1}(\sec x-\tan x)\), then \(\frac{d y}{d x}=\)MHT CET 2022 Medium
- The values of in satisfying the equation are ________MHT CET 2019 Easy
More PYQs from MHT CET
- Two rods of same material and volume having circular cross-section are subjected to tension T. Within the elastic limit, same force is applied to both the rods. Diameter of the first rod is half of the second rod, then the extensions of first rod to second rod will be in the ratioMHT CET 2020 Easy
- The moment of inertia of a circular disc of radius \(2 \mathrm{~m}\) and mass \(1 \mathrm{~kg}\) about an axis \(\mathrm{XY}\) passing through its center of mass and perpendicular to the plane of the disc is \(2 \mathrm{~kg} \mathrm{~m}^2\). The moment of inertia about an axis parallel to the axis \(\mathrm{XY}\) and passing through the edge of the disc isMHT CET 2021 Medium
- The lines \(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \quad\) and \(\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}\)MHT CET 2023 Easy
- Identify the monosaccharide containing only one asymmetric carbon atom in its molecule.MHT CET 2018 Medium
- What is the formula of calamine?MHT CET 2020 Easy
- Calculate the work done when 2 moles of an ideal gas expand from a volume of \(5 \mathrm{dm}^3\) to \(7 \times 10^{-3} \mathrm{~m}^3\) against a constant external pressure of \(2.02 \times 10^5 \mathrm{Nm}^{-2}\).MHT CET 2022 Easy