Prove the identity sin2x1+tan2x≡2sinxcos3x\frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x1+tan2xsin2x≡2sinxcos3x
The rate of airflow R R\,R into a mechanical respirator, in litres per second, is modeled by the function R(t)=10sin6t1+tan23tR(t) = \frac{10 \sin 6t}{1 + \tan^2 3t}R(t)=1+tan23t10sin6t where t t\,t is the time in seconds. Find an expression for the total volume of air V=∫R(t) dtV = \int R(t) \, dtV=∫R(t)dt.
Practise Edexcel A Level Maths 11.3 Using Trigonometric Identities with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.