Top answers

Prove cosec2A-cot2A=tanA

Cosec2A - cot2A= tanA Left hand side=1/sin2A - cos2A/sin2A =(1- cos2A)/sin2A =(1-(1- 2 sin^2⁡ A)/ 2sinAcosA =(1-1 + ( 2 sin^2⁡ A))/ 2sinAcosA =sinA/cosA =tanA Therefore left hand side of the equation is equa...
ST
Answered by Sherin T. • Maths tutor
14184 Views

A curve is defined by parametric equations: x = t^(2) + 2, and y = t(4-t^(2)). Find dy/dx in terms of t, hence, define the gradient of the curve at the point where t = 2.

dy/dx = (dy/dt)/(dx/dt) y = t(4-t 2 ), then using differentiation of y with respect to t, dy/dt = 4 - 3t 2 x = t 2 + 2, then using differentiation of x with respect to t, dx/dt = 2t Find dy/dx by dividing dy...
MW
Answered by Micah W. • Maths tutor
5897 Views

Express 3sin(2x) + 5cos(2x) in the form Rsin(2x+a), R>0 0<a<pi/2

Start by expanding out Rsin(2x+a) using the addition formula for sin, sin(A+B) = sin(A)cos(B)+cos(A)sin(B). Substituting 2x = A and a= b, we get that Rsin(2x+a) = R(sin(2x)cos(a) + cos(2x)sin(a)) = Rcos(a)si...
MF
Answered by Michael F. • Maths tutor
10410 Views

Solve the simultaneous equations: y=x+1, x^2+y^2=13

We already have an expression for y, so we can substitute this in:x 2 +(x+1) 2 =x 2 +(x+1)(x+1) = x 2 +x 2 +2x+1=2x 2 +2x+1 and hence 2x 2 +2x+1=13 and so 2x 2 +2x-12=0Now look for common factors. Here we ca...
LC
Answered by Lauren C. • Maths tutor
7826 Views

Using trigonometric identities, show that (cos(x) + sin(x))^2=1+sin(2x)

First being by expanding the brackets of the formula on the left: (cos(x) + sin(x)) 2 = (cos(x) + sin(x))*(cos(x) + sin(x)) = cos 2 (x)+2cos(x)sin(x)+sin 2 (x).Now we must use our understanding of trigonomet...
Answered by • Maths tutor
6915 Views