MHT CET · Maths · Trigonometric Equations
If \(\frac{\sin (A+B)}{\sin (A-B)}=\frac{\cos (C+D)}{\cos (C-D)}\), then \(\tan A \cot B=\)
- A \(\cot C \cot D\)
- B \(-\tan C \tan D\)
- C \(\tan C \tan D\)
- D \(-\cot C \cot D\)
Answer & Solution
Correct Answer
(D) \(-\cot C \cot D\)
Step-by-step Solution
Detailed explanation
\(\frac{\sin (A+B)}{\sin (A-B)}=\frac{\cos (C+D)}{\cos (C-D)}\)
\(\therefore \frac{\sin (A+B)+\sin (A-B)}{\sin (A+B)-\sin (A-B)}=\frac{\cos (C+D)+\cos (C-D)}{\cos (C+D)-\cos (C-D)}\)
\(\therefore \frac{2 \sin A \cos B}{2 \cos A \sin B}=\frac{2 \cos C \cos D}{-2 \sin C \sin D}\)
\(\quad \tan A \cot B=-\cot C \cot D\)
\(\therefore \frac{\sin (A+B)+\sin (A-B)}{\sin (A+B)-\sin (A-B)}=\frac{\cos (C+D)+\cos (C-D)}{\cos (C+D)-\cos (C-D)}\)
\(\therefore \frac{2 \sin A \cos B}{2 \cos A \sin B}=\frac{2 \cos C \cos D}{-2 \sin C \sin D}\)
\(\quad \tan A \cot B=-\cot C \cot D\)
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
- If the line \(\bar{r}=(\hat{\imath}-2 \hat{\jmath}+3 \hat{k})+\lambda(2 \hat{\imath}+\hat{\jmath}+2 \hat{k})\) is parallel to the plane \(\bar{r} \cdot(3 \hat{\imath}-2 \hat{\jmath}-m \hat{k})=5\), then value of \(m\) isMHT CET 2020 Easy
- If \(\mathrm{A}(-4,5, \mathrm{P}), \mathrm{B}(3,1,4)\) and \(\mathrm{C}(-2,0, \mathrm{q})\) are the vertices of a triangle \(A B C\) and \(G(r, q, 1)\) is its centroid, then the value of \(2 p+q-r\) is equal toMHT CET 2024 Easy
- If thenMHT CET 2018 Easy
- \(A(\propto)\left[\begin{array}{cc}\cos \propto & \sin \propto \\ -\sin \propto & \cos \propto\end{array}\right]\), then \(\left[A^2(\propto)\right]^{-1}=\)MHT CET 2021 Medium
- The foot of the perpendicular drawn from the origin to the plane \(x+y+3 z-4=0\)
isMHT CET 2020 Easy - If two sides of a square are \(4 x+3 y-20=0\) and \(4 x+3 y+15=0\), then the area of the square isMHT CET 2024 Easy
More PYQs from MHT CET
- If decomposition of hydrogen peroxide is a first order reaction, it's rate law equation can be represented asMHT CET 2021 Easy
- Which gives \(+7\) oxidation state?MHT CET 2010 Medium
- If the Vant Hoff factor for solution is the degree of dissociation isMHT CET 2019 Medium
- The thermal conductivity of a rod is \(2 .\) What is its thermal resistivity?MHT CET 2007 Hard
- The value of \({ }^{47} C_4+\sum_{j=1}^5{ }^{(52-j)} C_3\) isMHT CET 2025 Medium
- The volume of a tetrahedron whose vertices are \(\mathrm{A} \equiv(-1,2,3), \mathrm{B} \equiv(3,-2,1)\), \(\mathrm{C} \equiv(2,1,3)\) and \(\mathrm{D} \equiv(-1,-2,4)\) isMHT CET 2020 Easy