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)`

Prove that: sin^(-1)(3/5)=tan^(-1)(3/4)

The angle between the curves y^2=x and x^2=y at (1,\ 1) is tan^(-1)4/3 (b) tan^(-1)3/4 (c) 90 (d) 45

The angle between the pair of straight lines 2x^2+5xy+2y^2+3x+3y+1=0 is (A) cos^(-1)(4/5) (A) tan^(-1)(4/5) (A) pi/2 (D) 0

Prove that : tan^(-1)(1/2) + tan^(-1)(1/3) = tan^(-1)(3/5) + tan^(-1)(1/4) = pi/4

Prove that sin ^(-1).(3)/(5) = tan ^(-1) .(3)/(4) .

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)

The gradient of the common tangent to the two curves y=x^2-5x+6 and y=x^2+x+1 is: -1/3 (b) -2/3 (c) -1 (d) -3

The length of the tangent of the curve y=x^(2)+1 at (1 ,3) is (A) sqrt(5) (B) 3sqrt(5) (C) 1/2 (D) 3(sqrt(5))/(2)

The angle between the normals of ellipse 4x^2 + y^2 = 5 , at the intersection of 2x+y=3 and the ellipse is (A) tan^(-1) (3/5) (B) tan^(-1) (3/4) (C) tan^(-1) (4/3) (D) tan^(-1) (4/5)

Prove that: sin^(-1)(-4/5)=tan^(-1)(-4/3)=cos^(-1)(-3/5)-pi