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Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds2 Marks
Question
Prove that: $\frac{\sin\text{x}+\sin2\text{x}}{1+\cos\text{x}+\cos2\text{x}}=\tan\text{x}$
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Answer

$\text{LHS}=\frac{\sin\text{x}+\sin2\text{x}}{1+\cos\text{x}+\cos2\text{x}}$ $=\frac{\sin\text{x}+2\sin\text{x},\cos\text{x}}{\cos\text{x}+(1+\cos2\text{x})}$ $=\frac{\sin\text{x}(1+2\cos\text{x})}{\cos\text{x}+2\cos\text{x}}$ $=\frac{\sin\text{x}(1+2\cos\text{x})}{\cos\text{x}(1+2\cos\text{x})}$ $=\frac{\sin\text{x}}{\cos\text{x}}$ $=\tan\text{x}=\text{RHS}$

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