Prove that `(asintheta+bcostheta)^2+(acostheta-bsintheta)^2=a^2+b^2`

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

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

If tantheta=a/b , then (asintheta+bcostheta)/(asintheta-bcostheta) is equal to (a) (a^2+b^2)/(a^2-b^2) (b) (a^2-b^2)/(a^2+b^2) (c) (a+b)/(a-b) (d) (a-b)/(a+b)

If asintheta+bcostheta=c then prove that acostheta-bsintheta=sqrt(a^2+b^2-c^2)

If A B C having vertices A(acostheta_1,asintheta_1),B(acostheta_2asintheta_2),a n dC(acostheta_3,asintheta_3) is equilateral, then prove that costheta_1+costheta_2+costheta_3=sintheta_1+sintheta_2+sintheta_3=0.

If acosheta+bsintheta=4 & asintheta - bcostheta= 3 then a^2+b^2

If DeltaABC having vertices A(acostheta_1, asintheta_1), B(acostheta_2, asintheta_2), and C(acostheta_3, asintheta_3) are equilateral triangle, then prove that cos theta_1 + costheta_2 + cos theta_3 =0 and sintheta_1 + sintheta_2 + sintheta_3 =0

If (a costheta_1,asintheta_1),(acostheta_2,a sintheta_2) , and (acostheta_3a sintheta_3) represent the vertces of an equilateral triangle inscribed in a circle. Then.

int_0^(pi/2) (a+bsintheta)^3costheta d theta

If acostheta-bsintheta=c , then asintheta+bcostheta= (a) +-sqrt(a^2+b^2+c^2) (b) +-sqrt(a^2+b^2-c^2) (c) +-sqrt(c^2-a^2-b^2) (d) None of these