Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Equations1 Mark
Question
Write the values of x in $[0,\pi]$ for which $\sin2\text{x},\frac{1}{2}$ and $\cos2\text{x}$ are in A.P.
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Answer
We want to find the value of x for which $\frac{1}{2}-\sin2\text{x}=\cos2\text{x}-\frac{1}{2}$ $\Rightarrow\cos2\text{x}+\sin2\text{x}=1$ $\Rightarrow1-2\sin^2\text{x}+2\sin\text{x}\cos\text{x}=1$ $\Rightarrow2\sin\text{x}(\cos\text{x}-\sin\text{x})=0$ $\Rightarrow\sin\text{x}=0$ or $\cos\text{x}=\sin\text{x}$ $\Rightarrow\text{x}=0,\frac{\pi}{4},\pi$
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