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Prove that the equation p cos x - q sin ...

Prove that the equation p cos x - q sin x = r admits solution for x if and only if `-sqrt(p^2 + q^2) lt r lt sqrt(p^2 + q^2)`

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PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
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  2. Find the number of distinct solutions of sec x + tan x =sqrt3, where 0...

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  3. Prove that the equation p cos x - q sin x = r admits solution for x if...

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  4. let [] denotes the greatest integer less than or equal to x and f(x) =...

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  6. Solve the equation (sin x + cos x)^(1 + sin2x) = 2, when -pi le x le p...

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  7. Find the most general solutions for 2^sinx + 2^cosx = 2^(1 - 1/sqrt2).

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  8. Solve 3 cos^2 theta - 2 sqrt3 sin theta cos theta - 3 sin^2 theta = 0

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  9. Find the number of solution for sin 5theta cdot cos 3theta = sin 9thet...

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  10. Find the general solution of the equation sin 3 alpha = 4 sin alpha si...

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  11. A triangle ABC is such that sin (2A + B) = 1/2 . If A,B,C are in A.P.,...

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  12. If cos^-1 x/a + cos^-1 y/b = alpha , then show x^2/a^2 + y^2/b^2 - (2x...

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  13. If cos^-1 lambda + cos^-1 mu + cos^-1 gamma = 3 pi, then find the valu...

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  14. If sum(i=1)^(2n) sin^-1xi = npi then find the value of sum(i = 1)^(2n)...

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  15. If sin^-1x + sin^-1 y + sin^-1 z = pi, prove that x^4 + y^4 + z^4 + 4x...

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  16. Find the value of tan{1/2 sin^-1((2x)/(1+x^2)) + 1/2cos^-1 ((1-y^2)/(1...

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  17. If sin^-1x + sin^-1 y + sin^-1 z = (3 pi)/2, then find the value of su...

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  18. Solve for x : If [sin^-1(cos^-1(sin^-1(tan^-1x)))]=1, where [cdot] d...

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  19. If xgamma is given by, x(gamma + 1) = sqrt(1/2(1+xgamma) Then show :...

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  20. Solve sin x + sqrt3 cos x = sqrt2

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