What is the double angle formula?
The double angle formula is how to combine/split trigonometric functions so that they can be integrated or simplified using identities. For example, cos (a+b)= cos(a)cos(b) - sin(a)sin(b) , which can be extended to cos(2a)= cos^2(a)-sin^2(a). This is useful for instances where you are required to integrate/differentiate sin^2(x) for example, as using the identity cos^2(x)+sin^2(x)=1 means that the double angle formula can rearrange cos(2x) into 1-2sin^2(x),meaning that sin^2(x) =(cos(2x)-1)/2. This can be integrated with ease into sin(2x)/4 -x/2 +c.
RW
Related Maths A Level answers
All answers ▸Given y=2x^4-1+x^1/2, solve dy/dx
Show how you can rewrite (x+1)(x-2)(x+3) into the form of ax^3 + bx^2 + cx + d
Given y = 2x(x^2 – 1)^5, show that dy/dx = g(x)(x^2 – 1)^4 where g(x) is a function to be determined.
The point P (4, –1) lies on the curve C with equation y = f( x ), x > 0, and f '(x) =x/2 - 6/√x + 3. Find the equation of the tangent to C at the point P , giving your answer in the form y = mx + c. Find f(x)