AP EAMCET · Maths · Properties of Triangles
For \(A, B\) and \(C\), if \(A+B+C=0\), then \(\sin (2 A)+\sin (2 B)+\sin (2 C)\) is equal to
- A \(4 \sin (A) \cdot \sin (B) \cdot \sin (C)\)
- B \(2 \sin (A) \cdot \sin (B) \cdot \sin (C)\)
- C \(-4 \sin (A) \cdot \sin (B) \cdot \sin (C)\)
- D \(-2 \sin (A) \cdot \sin (B) \cdot \sin (C)\)
Answer & Solution
Correct Answer
(C) \(-4 \sin (A) \cdot \sin (B) \cdot \sin (C)\)
Step-by-step Solution
Detailed explanation
For \(A+B+C=0\) \(\begin{aligned} \sin 2 A+ & \sin 2 B+\sin 2 C \\ & =2 \sin (A+B) \cos (A-B)+2 \sin C \cos C \\ & =-2 \sin C \cos (A-B)+2 \sin C \cos (A+B) \\ & =-2 \sin C[\cos (A-B)-\cos (A+B)] \\ & =-2 \sin C[2 \sin A \sin B] \\ & =-4 \sin A \sin B \sin C. \end{aligned}\)
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
- AP EAMCET 2022 Medium
- The set of all real numbers satisfying the inequation \(x^2-|x+2|+x>0\) isAP EAMCET 2019 Medium
- The eccentricity of the conic \(36 x^2+144 y^2-36 x-96 y-119=0\) isAP EAMCET 2004 Easy
- If the probability function of a random variable \(X\) is defined by \(P(X=k)=a\left(\frac{k+1}{2^k}\right)\) for \(k=0,1,2,3,4,5\), then the probability that \(X\) takes a prime value isAP EAMCET 2018 Hard
- If the origin is the centroid of the triangle for which \((-2,3,4)\) and \((3,-1,5)\) are two vertices, then the third vertex isAP EAMCET 2021 Easy
- From a point on the level ground, the angle of elevation of the top of a pole is \(30^{\circ}\) on moving 20 metres nearer, the angle of elevation is \(45^{\circ}\). Then, the height of the pole (in metres), isAP EAMCET 2002 Medium
More PYQs from AP EAMCET
- Freezing compartment of a refrigerator is at \(0^{\circ} \mathrm{C}\) and room temperature is \(27.3^{\circ} \mathrm{C}\). Work done by the refrigerator to freeze \(1 \mathrm{~g}\) of water at \(0^{\circ} \mathrm{C}\) is \(\left(L_{\text {ice }}=80 \mathrm{cal} \mathrm{g}^{-1}\right)\)AP EAMCET 2018 Easy
- A car travels with a speed of . Rain drops are falling at a constant speed vertically. The traces of the rain on the side windows of the car make an angle of with the vertical. The magnitude of the velocity of the rain with respect to the car isAP EAMCET 2022 Medium
- \(\int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x\) is equal to :AP EAMCET 2003 Medium
- The number of different signals which can be given from 7 different coloured sheets, taking one or more at a time isAP EAMCET 2017 Medium
- A solid float such that its \((1 / 3)\) rd part is above water surface. Then, the density of solid isAP EAMCET 2021 Medium
- Total number of angular nodes of orbitals associated with third shell \((n=3)\) of an atom isAP EAMCET 2023 Easy