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a) tan(A+B)=(tanA+tanB)/(1-tanAtanB) So, tan(2x)=[tan(x)+tan(x)]/[1-(tanx)(tanx)]. Therefore, tan(2x)=[2tan(x)]/[1-tan^2(x)] = 2p/(1-p^2). b) cos(x)=1/sec(x). Using other trigonometric identities, we know...

These are two really useful rules for differentiating functions. We use the chain rule when differentiating a 'function of a function', like f(g(x)) in general. We use the product rule when differentiatin...

For the 1st part of the question: use the double angle formula to rewrite cos(2x) = cos^2(x) - sin^2(x). Then use the basic identity to write cos^2(x) = 1-sin^2(x), hence cos(2x) = 1-2sin^2(x). Plug the r...

Split the equation into two : one that you are going to integrate, and the other one you want to differentiate. then, apply formula uv - integral(v * du)

Finding normals and tangents to curves is a very common question in A-level maths papers, especially core 3 modules, giving between 5-8 marks depending on complexity. In order to start this question, the ...