Compound and double angle formulaeEdexcel A-Level Maths: Subtopic test

1. 1
   Angles $A$ and $B$ are acute, with $\sin A=\frac{3}{5}$ and $\cos B=\frac{5}{13}$.

   (a)

   Find the value of $\sin(A+B)$.

   [1 mark]

   • A$\frac{56}{65}$
   • B$-\frac{33}{65}$
   • C$\frac{63}{65}$
   • D$\frac{3}{13}$

   (b)

   Find the value of $\cos(A+B)$.

   [1 mark]

   • A$\frac{16}{65}$
   • B$-\frac{16}{65}$
   • C$\frac{56}{65}$
   • D$\frac{4}{13}$

   (c)

   Find the exact value of $\tan(A+B)$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The angle $x$ is acute and $\tan x=\frac{3}{4}$.

   (a)

   Find the value of $\tan2x$.

   [1 mark]

   • A$\frac{24}{25}$
   • B$\frac{7}{25}$
   • C$\frac{3}{2}$
   • D$\frac{24}{7}$

   (b)

   Find the value of $\cos2x$.

   [1 mark]

   • A$\frac{7}{25}$
   • B$\frac{24}{25}$
   • C$\frac{18}{25}$
   • D$-\frac{7}{25}$

   (c)

   Hence find the exact value of $\cos4x$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Consider the equation $\cos2\theta+3\sin\theta=2$, where $0\le\theta<360^\circ$.

   (a)

   Show that the equation can be written as $2\sin^2\theta-3\sin\theta+1=0$.

   [3 marks]

   (b)

   Hence solve the equation, giving all solutions in the interval $0\le\theta<360^\circ$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Let $f(\theta)=\sqrt3\cos\theta+\sin\theta$, where $\theta$ is measured in degrees.

   (a)

   (i) Write $f(\theta)$ in the form $R\cos(\theta-\alpha)$, where $R>0$ and $0<\alpha<90^\circ$.
   (ii) Hence solve $f(\theta)=1$ for $0\le\theta<360^\circ$.

   [6 marks]

   (b)

   (i) Write down the maximum value of $f(\theta)$ and the smallest positive value of $\theta$ at which it occurs.
   (ii) Solve $f(\theta)=\sqrt2$ for $0\le\theta<360^\circ$.

   [6 marks]

   Total for question 4: 12 marks

End of questions