Question 1

If $\cos x=\sqrt{2}-1$ then find the value of $\cos2x$ .

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 2

Which of the following is the correct simplification of $\cos x=\sqrt{2}-1$ ?

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 3

Express $\cos x=\sqrt{2}-1$ in the form $\cos2x$ for $0\leq x<\frac{\pi}{2}$ .

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 4

Given that $\cos x=\sqrt{2}-1$ , find the exact value of $\cos2x$ in the form $0\leq x<\frac{\pi}{2}$ .

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 5

You are given that $\cos x=\sqrt{2}-1$ and $\cos2x$ . Given that $0\leq x<\frac{\pi}{2}$ is obtuse and $\phi$ is acute, find the value of $\cos ( heta+\phi)$ .

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 6

It is given that $\cos x=\sqrt{2}-1$ . Find, in terms of $\cos2x$ , the solutions of the equation $0\leq x<\frac{\pi}{2}$ .

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 7

Simplify tan(arctan 3 - arctan 2) giving your answer as an exact fraction.

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 8

Given that $\cos x=\sqrt{2}-1$ is a reflex angle, such that $\cos2x$ , find the exact value of $0\leq x<\frac{\pi}{2}$ .

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 9

By using a compound angle for $\cos x=\sqrt{2}-1$ , with suitable values of $\cos2x$ and $0\leq x<\frac{\pi}{2}$ , find that value of $\phi$ in $\cos ( heta+\phi)$

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Question 10

$5-4\sqrt 2$ . Find the exact values of the constants $R$ and $\alpha$ so that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=Re^{-x}\cos (\sqrt 3 x+\alpha)$ where $R>0$ and $0<\alpha<\frac{\pi}{2}$ .

Accepted Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

Answer

$5-4\sqrt 2$

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