Question
Prove the following:
$\cot4\text{x}(\sin5\text{x}+\sin3\text{x})=\cot4\text{x}(\sin5\text{x}-\sin3\text{x})$
$\cot4\text{x}(\sin5\text{x}+\sin3\text{x})=\cot4\text{x}(\sin5\text{x}-\sin3\text{x})$
$=\frac{\cos4\text{x}}{\sin4\text{x}}[2\sin4\text{x}\cos\text{x}]$
$=2\cos4\text{x}\cos\text{x}$
$\text{R.H.S.}=\cot4\text{x}(\sin5\text{x}-\sin3\text{x})$
$\text{L.H.S.} = \text{R.H.S.}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| Subject | Mathematics | Physics | Chemistry |
| Mean | 42 | 32 | 40.9 |
| Standard deviation | 12 | 15 | 20 |
Which of these three subjects shows the highest variability in marks and which shows the lowest?
$\sin\text{A}\sin(\text{B}-\text{C})+\sin\text{B}\sin(\text{C}-\text{A})+\sin\text{C}\sin(\text{A}-\text{B})=0$
| x | 4.5 | 14.5 | 24.5 | 34.5 | 44.5 | 54.5 | 64.5 |
| f | 1 | 5 | 12 | 22 | 17 | 9 | 4 |