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If A + B + C + D = 2pi, prove that: cos ...

If `A + B + C + D = 2pi`, prove that: `cos A + cos B + cos C + cos D`
`=-4"cos"(A+B)/(2)"cos"(A+C)/(2)"cos"(A+D)/(2)`

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MODERN PUBLICATION-TRIGONOMETRY-Revision Exerise
  1. Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2

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  2. If (s in^4theta)/a+(cos^4theta)/b=1/(a+b) , prove that (s in^8theta)/...

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  3. If at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2) , where alpha!=beta...

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  4. If alphaa n dbeta are the solutions of acostheta+bs intheta=c , then s...

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  5. If alpha and beta are the solution of the equation, a tantheta+bsecth...

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  6. If tanbeta=(Q"sin"alpha)/(P+Qcosalpha) Prove that "tan"(alpha-beta)=...

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  7. Prove that: cotthetacot2theta+cottheta2cot3theta+2=cottheta(cottheta-c...

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  8. Prove that:(cos 2A cos 3A -cos 2A cos 7A + cos A cos 10A)/("sin" 4A si...

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  9. If theta(1),theta(2),theta(3),".......",theta(n) are in AP whose commo...

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  10. If A+B+C = pi prove that cos 4A + cos 4B + cos 4C = -1 + 4 cos 2A co...

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  11. If A+B+C=pi, prove that : sin, (B+C)/(2) + sin, (C+A)/(2) + sin, (A+B)...

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  12. If A + B + C = 180^(@) prove that: (i) "sin" (B+C-A) + "sin"(C+ A-B)...

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  13. Prove that the triangle ABC is equilateral if cotA+cotB+cotC=sqrt3

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  14. If A + B + C + D = 2pi, prove that: cos A + cos B + cos C + cos D =...

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  15. If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/...

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  16. If x y+y z+x z=1,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y...

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  17. Find the solutions x in [0,2pi] of:"sin" 2x – 12 ("sin" x - cos x) + 1...

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  18. Solve : (i) cos 3theta + 8 cos^(3) theta = 0 (ii) "tan" (pi cot x) ...

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  19. Prove that the values of the function("sin"xcos3x)/(cosx"sin"3x)do not...

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  20. If p(1),p(2),p(3) are the altitues of a triangle from the vertieces A,...

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