Question 1

Split the following expression into partial fractions: $\frac{f(x)}{(ax+b)(cx+d)}$

Accepted Answer

$\frac{A}{ax+b}+\frac{B}{cx+d}$

Answer

$\frac{A}{(ax+b)^2}+\frac{B}{cx+d}$

Answer

$\frac{A}{ax+b}+\frac{A}{(ax+b)^2}+\frac{B}{cx+d}$

Answer

$\frac{A}{ax+b}+\frac{B}{(cx+d)^2}$

Question 2

Split the following expression into partial fractions: $\frac{f(x)}{(ax+b)(cx+d)^2}$

Accepted Answer

$\frac{A}{ax+b}+\frac{B}{cx+d}+\frac{C}{(cx+d)^2}$

Answer

$\frac{A}{ax+b}+\frac{C}{(cx+d)^2}$

Answer

$\frac{A}{(ax+b)^2}+\frac{C}{(cx+d)^2}$

Answer

$\frac{A}{ax+b}+\frac{B}{cx+d}+\frac{C}{(ax+b)^2}$

Question 3

$\sin(A\pm B)=?$

Accepted Answer

$\sin A \cos B \pm \cos A \sin B$

Answer

$\cos A \cos B \mp \sin A \sin B$

Answer

$\sin A \cos B \mp \cos A \sin B$

Answer

$\cos A \cos B \pm \sin A \sin B$

Question 4

$\cos(A\pm B)=?$

Accepted Answer

$\cos A \cos B \mp \sin A \sin B$

Answer

$\sin A \cos B \mp \cos A \sin B$

Answer

$\cos A \cos B \pm \sin A \sin B$

Answer

$\sin A \cos B \pm \cos A \sin B$

Question 5

$	an(A\pm B)=?$

Accepted Answer

$\frac{	an A \pm 	an B}{1 \mp 	an A 	an B}$

Answer

$\frac{	an A \pm 	an B}{1 \pm 	an A 	an B}$

Answer

$\frac{	an A \mp 	an B}{1 \mp 	an A 	an B}$

Answer

$\frac{	an A \mp 	an B}{1 \mp 	an A 	an B}$

Question 6

$\sin 2A = ?$

Accepted Answer

$2\sin A \cos A$

Answer

$\cos^2 A - \sin^2 A$

Answer

$1-2\sin^2 A$

Answer

$2\cos^2 A - 1$

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