The angle between the tangents to the curves `y=x^2a n dx=y^2a t(1,1)` is `cos^(-1)(4/5)` (b) `sin^(-1)(3/5)` `tan^(-1)(3/4)` (d) `tan^(-1)(1/3)`

The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the point (1,3) is.

The equation of the tangent to the curve y = (x^(3))/(5) " at " (-1, -(1)/(5)) is

Tangent and normal are drawn at the point P-=(16 ,16) of the parabola y^2=16 x which cut the axis of the parabola at the points Aa n dB , rerspectively. If the center of the circle through P ,A ,a n dB is C , then the angle between P C and the axis of x is (a)tan^(-1)(1/2) (b) tan^(-1)2 (c)tan^(-1)(3/4) (d) tan^(-1)(4/3)

2tan^(-1)(-2) is equal to (a) -cos t^(-1)((-3)/5) (b) -pi+cos^(-1)3/5 (c) -pi/2+tan^(-1)(-3/4) (d) -picot^(-1)(-3/4)

Prove that cos^(-1)((4)/(5))+tan^(-1)((3)/(5))=tan^(-1)((27)/(11))

The angle of intersection between the curves x^(2) = 4(y +1) and x^(2) =-4 (y+1) is

Find the equation of tangent to the curve y=sin^(-1)(2x)/(1+x^2)a tx=sqrt(3)

The angle between the pair of lines whose equation is 4x^2+10 x y+m y^2+5x+10 y=0 is (a) tan^(-1)(3/8) (b) tan^(-1)(3/4) (c) tan^(-1){2(sqrt(25-4m))/(m+4)},m in R (d) none of these

A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to the parabola at Aa n dB meet the y-axis at A_1a n dB_1 , respectively. If the area of trapezium AA_1B_1B is equal to 12 a^2, then the angle subtended by A_1B_1 at the focus of the parabola is equal to 2tan^(-1)(3) (b) tan^(-1)(3) 2tan^(-1)(2) (d) tan^(-1)(2)

Prove : 2 sin ^(-1) "" 3/5 = tan ^(-1) ""(24)/(7)