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If (a+b+c)(b+c-a)=3bc then show that ang...

If (a+b+c)(b+c-a)=3bc then show that `angleA=pi/3`

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PATHFINDER-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove that for a triangle ABC, (a^2-b^2-c^2) tan A+(a^2-b^2+c^2)tan B=...

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  2. In any triangle ABC prove that sin2A+sin2B+sin2C=(abc)/(2R^3)

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  3. If (a+b+c)(b+c-a)=3bc then show that angleA=pi/3

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  4. If the angles of the triangle ABC are in A.P. and b:c=sqrt3:sqrt2 then...

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  5. For triangleABC prove that (sin A+sin B)(sin B+sin C)(sin C+sin A)gtsi...

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  6. If in triangleABC, (2cosA)/a+(cosB)/b+(2cosC)/c=a/(bc)+b/(ca) then de...

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  7. If sin A/sin C=sin(A-B)/sin(B-C) then show that a^2,b^2,c^2 are in ari...

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  8. a,b,c are the lengths of sides of triangleABC and 1/(a+c)+1/(b+c)=3/(a...

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  9. In triangleABC show that a=bcosC+ccosB

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  10. In triangleABC if angleA=60^@ then show that (b+c)/a=2cos((B-C)/2)

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  11. For any triangle ABC show that a sin(B-C)+bsin(C-A)+csin(A-B)=0

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  12. In triangleABC angleC=90^@ then show that (a^2+b^2)/(a^2-b^2)sin(A-B)...

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  13. In triangleABC if acos^2(C/2)+c cos^2(A/2)=3b/2 then show that a,b,c a...

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  14. In any triangle ABC show that b^2sin2C+c^2sin 2B=abc/R

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  15. In any triangle ABC show that sinA+sinB gt sin C

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  16. Prove that for any triangle ABC,(cosBcosC)/bc+(cosCcosA)/ca+(cosAcosB)...

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  17. For any triangle ABC prove that (b-c)cot(A/2)+(c-a)cot(B/2)+(a-b)cot(C...

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  18. for any triangleABC show that (b^2-c^2)/(cosB+cosC)+(c^2-a^2)/(cosC+co...

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  19. if in a triangle ABC ,a^2,b^2,c^2 are in A.P. then show that cotA,cotB...

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  20. In triangle ABC tan(A/2), tan(B/2) and tan (C/2) are in A.P. then prov...

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