Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions1 Mark
Question
If $3\sin\text{x}+5\cos\text{x}=5,$ then write the value of $5\sin\text{x}-3\cos\text{x}.$
✓
Answer
$3\sin\text{x}+5\cos\text{x}=5$ (Given) Squaring both the side: $9\sin^2\text{x}+25\cos^2\text{x}+30\sin\text{x}\cos\text{x}=25$ $30\sin\text{x}\cos\text{x}=25-9\sin^2\text{x}-25\cos^2\text{x}\cdots(1)$ We have to find the value of $5\sin\text{x}-3\cos\text{x}.$ $(5\sin\text{x}-3\cos\text{x})^2=25\sin^2\text{x}+9\cos^2\text{x}-30\sin\text{x}\cos\text{x}$ $(5\sin\text{x}-3\cos\text{x})^2=25\sin^2\text{x}+6\cos^2\text{x}-(25-9\sin^2\text{x}-25\cos^2\text{x})$ [From (1)] $(5\sin\text{x}-3\cos\text{x})^2=34\sin^2\text{x}+34\cos^2\text{x}-25$ $(5\sin\text{x}-3\cos\text{x})^2=34-25$ $(\because\sin^2\text{x}+\cos^2\text{x}=1)$ $(5\sin\text{x}-3\cos\text{x})^2=9$ $5\sin\text{x}-3\cos\text{x}=\pm3$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.