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(a+b+c)[tan A/2 + tanB/2]

  1. (a+b+c)[tan A/2 + tanB/2]

Grade:12

1 Answers

Lab Bhattacharjee
121 Points
5 years ago
Use HINT: $$\dfrac a{\sin A}=\cdots=2R\\ \text{ and } \sin A+\sin B+\sin C=2\sin\dfrac A2\cos\dfrac A2+2\sin\dfrac{B+C}2\cos\dfrac{B-C}2$$ $$\\ \text{ But } \sin\dfrac{B+C}2=\cos\dfrac A2\text{ and }\cos\dfrac{B+C}2=\sin\dfrac A2$$ $$\\ \implies a+b+c=2R[2\cos\dfrac A2\left(\cos\dfrac{B+C}2+\cos\dfrac{B-C}2\right )]=2R[4\cos\dfrac A2\cos\dfrac B2\cos\dfrac C2]$$

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