AP EAMCET · Maths · Straight Lines
Number of triangles in which \(\tan A+\tan B+\tan C=\cot A+\cot B+\cot C\) is
- A 1
- B \(\infty\)
- C 0
- D 2
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
Given, \(\tan A+\tan B+\tan C=\cot A+\cot B+\cot C\) It is possible only when one of the angle is \(45^{\circ}\) and sum of other two angles is \(90^{\circ}\). \[ \therefore \quad A+B+C=135^{\circ} < 180^{\circ} \] Hence, no triangle is possible.
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 \((1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}, \quad\) then \(\sum_{r=1}^{15} r \frac{a_r}{a_r-1}\) is equal toAP EAMCET 2005 Hard
- If the circles \(x^2+y^2-4 x+2 f y+1=0\) and \(x^2+y^2+\) \(2 \mathrm{gx}-4 \mathrm{y}-1=0\) cut orthogonally, then \(\mathrm{r}_1^2+\mathrm{r}_2^2-8=\)AP EAMCET 2023 Easy
- If the differential equation obtained by eliminating A,B from \(y=\left(\sin ^{-1} x\right)^2+A \cos ^{-1} x+B\) is \(\left(a-x^2\right) y^{\prime \prime}-x y^{\prime}=b\), then \(\frac{b+a}{b-a}=\)AP EAMCET 2022 Medium
- In \(\triangle \mathrm{ABC},(\cot \mathrm{A}+\cot \mathrm{B})(\cot \mathrm{B}+\cot \mathrm{C})(\cot \mathrm{C}+\cot \mathrm{A})=\)AP EAMCET 2023 Hard
- Let \(M\) and \(N\) be two invertible square matrices over \(R\) of order 2 such that \(N\) is diagonal. Then \(M N M^{-1}\) is diagonal ____AP EAMCET 2020 Medium
- Let \(f(x)= \begin{cases}\frac{5 e^{1 / x}+2}{3-e^{1 / x}}, & x \neq 0 \\ 0, & x=0\end{cases}\) Then at \(x=0, x f(x)\) and \(f(x)\) are respectivelyAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- The ground state energy of \(\mathrm{H}\) is equal toAP EAMCET 2017 Easy
- If \(x=\sec \theta-\cos \theta, y=\sec ^n \theta-\cos ^n \theta\) then \(\frac{d y}{d x}=\)AP EAMCET 2018 Medium
- The temperature of \(K\) at which \(\Delta G=0\), for a given reaction with \(\Delta H=-20.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(\Delta S=-50.0 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\) isAP EAMCET 2014 Easy
- The angular velocity of a body changes from \(6 \mathrm{rad} \mathrm{s}^{-1}\) to \(21 \mathrm{rad} \mathrm{s}^{-1}\) in a time of 1.5 s. If the moment of inertia of the body is \(100 \mathrm{~g} \mathrm{~m}^2\), then the rate of change of angular momentum of the body isAP EAMCET 2025 Medium
- Radius of gyration of a thin uniform rod of length ' \(L\) ' about an axis passing through its centre and perpendicular to its length isAP EAMCET 2025 Easy
- A \(1.0 \mathrm{~L}\) of aqueous solution contains \(1 \times 10^{-8} \mathrm{M} \mathrm{NaBr}, 1 \times 10^{-8} \mathrm{M} \mathrm{NaCl}\) and \(1 \times 10^{-8} \mathrm{M}\) NaI. To this solution, \(1 \times 10^{-10} \mathrm{M}\) aqueous \(\mathrm{AgNO}_3\) solution is added drop wise. The order of precipitation of \(\operatorname{Ag} X(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})\) is
\(\begin{aligned} & \left(K_{\mathrm{sp}}(\mathrm{AgCl})=1.8=10^{-10} ; K_{\mathrm{sp}}(\mathrm{AgBr})=5 \times 10^{-13} ;\right. \\ & \left.K_{\mathrm{sp}}(\mathrm{AgI})=8.3 \times 10^{-17}\right)\end{aligned}\)AP EAMCET 2022 Hard