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Evaluate (a+bcostheta)^2+(bsintheta)^2...

Evaluate `(a+bcostheta)^2+(bsintheta)^2`

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If cottheta=(b)/(a) ,show that (asintheta-bcostheta)/(asintheta+bcostheta)=(a^(2)-b^(2))/(a^(2)+b^(2)) .

Find the equations of the tangent and the normal to the curve (x^2)/(a^2)+(y^2)/(b^2)=1 at (acostheta,\ bsintheta) at the indicated points

Knowledge Check

  • If btantheta=a , the value of (asintheta-bcostheta)/(asintheta+bcostheta) (a) (a-b)/(a^2+b^2) (b) (a+b)/(a^2+b^2) (c) (a^2+b^2)/(a^2-b^2) (d) (a^2-b^2)/(a^2+b^2)

    A
    `(a-b)/(a^2+b^2)`
    B
    `(a+b)/(a^2+b^2)`
    C
    `(a^2+b^2)/(a^2-b^2)`
    D
    `(a^2-b^2)/(a^2+b^2)`

  • Let alpha, beta are the root of equation acostheta + bsintheta = c . Which of the following is/are true.

    A
    `sinalpha + sinbeta= (2bc)/(a^(2) + b^(2))`
    B
    `sinalpha + sinbeta= (2bc)/(b^(2) + c^(2))`
    C
    `tan'(alpha)/(2) + tan'(beta)/(2) = (b)/(a + c)`
    D
    `tan'(alpha)/(2) + tan"(beta)/(2) = (2b)/(a + c)`

  • Let alpha, beta are the root of equation acostheta + bsintheta = c . If alpha = 30^(@) and beta = 60^(@) such that a, b, c represent sides of a DeltaABC then

    A
    `ABC` is acute angle triangle
    B
    `ABC` is acute isosceles triangle
    C
    `ABC` is right angle triangle
    D
    `ABC` is obtuse angle triangle

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    If (9a)/(costheta)+(5b)/(sintheta)=56 and (9asintheta)/(cos^(2)theta)-(5bcostheta)/(sin^(2)theta)=0 If the value of [(9a)^(2/3)+(5b)^(2/3)]^(3)=(8K)^(2) Then K is ………..

    (i) Find the equation a circle passing through the point (2+3costheta,1+3sintheta) where 'theta' is a parameter. (ii) Prove that the equations x=atheta+bsintheta and y=asintheta-bcostheta represents a circle.

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