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The greatest angle of a cyclic quadrilat...

The greatest angle of a cyclic quadrilateral is three times the least. The other two angles are in the ratio 4:5. Find all the angles in radians,

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To solve the problem, we need to find the angles of a cyclic quadrilateral given certain conditions. Let's break down the solution step by step. ### Step 1: Define the angles Let: - The least angle \( A = y \) - The greatest angle \( C = 3y \) The other two angles \( B \) and \( D \) are in the ratio \( 4:5 \). Therefore, we can express them as: - \( B = 4x \) - \( D = 5x \)
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MODERN PUBLICATION-TRIGONOMETRY-Revision Exerise
  1. Prove that (1) the area of a sector of circle with radius r and centra...

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  2. The greatest angle of a cyclic quadrilateral is three times the least....

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  3. A wire of length 121 cm is bent so as to lie along the arc of a circle...

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  4. Prove that : (tanA)/(1-cotA)+(cotA)/(1-tanA)=1+secA" cosec"A

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  5. Eliminate alpha between the equations : ("sin"^(2)alpha)/(cosalpha)...

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  6. 3(sin x- cos x )^(4) + 6(sin x+ cos x )^(2) +4 (sin ^(6) x+ cos ^(6) x...

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  7. Given, "sin" x = -(3)/(7) and x belongs to the third quadrant, obtain ...

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  8. If sec A = x+(1)/(4x)prove that: sec A + tan A = 2x or (1)/(2x) ...

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  9. If "sin" x + "sin"^(2) x = 1 show that: cos^(4)x + cos^(2)x = 1 ...

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  10. If acostheta-b sintheta =c; prove that a sin theta + b costheta = pmsq...

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  11. Prove that"sin"(pi)/(14)"sin"(3pi)/(14)"sin"(5pi)/(14)"sin"(7pi)/(14)=...

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  12. Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2

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

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

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

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

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

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

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

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

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