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In any triangle A B C , prove that: a^3c...

In any triangle `A B C ,` prove that: `a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3a b c`

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MARVEL PUBLICATION-TRIGONOMETRIC FUNCTIONS-HARDER SOLVED EXAMPLES
  1. Triangle ABC is isosceles with AB = AC. If the radius of the cicum-cir...

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  2. If H is the orthocenter of DeltaABC and if AH = x, BH = y, CH = z, t...

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  3. In any triangle A B C , prove that: a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B...

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  4. If, in a /\ ABC, (2 cos A)/a + (cos B)/(b) + (2 cos C)/(c) = a/(bc) ...

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  5. If, in a /\PQR, right angled at R, tan (P/2) and tan (Q/2) are the r...

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  6. If, in Delta ABC, angle A,B,C are in A.P. And b : c = sqrt(3) : sqrt(2...

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  7. If in a triangle ABC, a=1+sqrt(3)cm,b=2 cm and angleC=60^(@) , then fi...

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  8. If the sides of a triangle are in the ratio 1 : sqrt(3) : 2, then its ...

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  9. If the angles of a triangle are in the ratio 4 : 1: 1, then the ratio ...

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  10. The perimeter of atriangle ABC is 6 times the arihmetic mean of the si...

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  11. A triangle park is enclosed on two sides by a fence and, on the third ...

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  12. If the radius of the circum-circle of an isosceles triangle PQR is equ...

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  13. In /\ABC, if 3 a=b + c, then cot(B/2) \ cot(C/2) =

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  14. In a /\ABC, if A,B,C are in A.P., then: a/c (sin 2C) + c/a (sin 2A) ...

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  15. If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi" , prove that " x^(2) + ...

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  16. If cos^(-1)(x/a) + cos^(-1) (y/b) = alpha show that : (x^2)/(a^2) - (...

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  17. Prove that tan{(pi)/4 + 1/2 Cos^(-1)((a)/(b))}+tan{((pi)/4-1/2 Cos^(-1...

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  18. If 0<a1<a2<ddot<an , then prove that tan^(-1)((a1x-y)/(x+a1y))+tan^(-1...

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  19. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

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  20. If alpha = tan^(-1) ((xsqrt(3))/(2y - x)) and beta = tan^(-1) ((2x - y...

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