Solve for `xa n dy :sqrt(3)sinx+cosx=8y-y^2-18 ,w h e r e0lt=xlt=4pi, y in R`

Solve the equation (sinx+cosx)^(1+sin2x)=2, when 0lt=xlt=pi

Write the range of the function f(x)=sin[x],w h e r e(-pi)/4lt=xlt=pi/4 .

Find the area of the region bounded by the x-axis and the curves defined by y=tanx(w h e r e-pi/3lt=xlt=pi/3) and y=cotx(w h e r epi/6lt=xlt=(3x)/2) .

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

Solve the differential equation: (dy)/(dx)=sqrt(4-y^(2)) , (-2 lt y lt 2)

If y=log(sinx-cosx) , then (dy)/(dx) at x=(pi)/(2) is :

Solve: (2+sinx)/(1+y) (dy)/(dx)=-cosx

Evaluate the following integral: int_0^9f(x)dx ,\ w h e r e\ f(x){sinx ,\ 0lt=xlt=pi//2 1,pi/2lt=xlt=3e^(x-3),\ 3lt=xlt=9