Question
$\text{b}(\text{c}\cos\text{A}-\text{a}\cos\text{C})=\text{c}^2-\text{a}^2$
$\text{RHS}=\text{c}^2-\text{a}^2$
$=\text{k}^2\sin^2\text{C}-\text{k}^2\sin^2\text{A}$
$=\text{k}^2(\sin^2\text{C}-\sin^2\text{A})$
$=\text{k}^2\sin(\text{C + A}).\sin(\text{C}-\text{A})$
$=\text{k}^2\sin(\pi-\text{B}).\sin(\text{C}-\text{A})$
$=\text{k}^2\sin\text{B}.\sin(\text{C}-\text{A})$
$=\text{k}\sin\text{B}.\text{k}\sin(\text{C}-\text{A})$
$=\text{bk}\sin(\text{C}-\text{A})$
$=\text{bk}(\sin\text{C}.\cos\text{A}-\sin\text{A}.\cos\text{C})$
$=\text{b}(\text{k}\sin\text{C}.\cos\text{A}-\text{k}\sin\text{A}.\cos\text{C})$
$=\text{b}(\text{c}\cos\text{A}-\text{a}\cos\text{C})=\text{LHS}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\frac{\text{a}}{1+\text{i}}+\frac{\text{a}}{(1+\text{i})^2}+\frac{\text{a}}{(1+\text{i})^3}+\ ...\ +\frac{\text{a}}{(1+\text{i})^\text{n}}.$
| Height in cm | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155 |
| Number of boys | 9 | 13 | 26 | 30 | 12 | 10 |