General solutions of the equations sinx=−12 and cosx=−32 is

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x=2nπ+π6

x=2nπ+5π6

x=2nπ+7π6

x=2nπ+11π6

answer is C.

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Detailed Solution

We have sinx=−12<0 and cosx=−32<0∴x belongs to 3rd quadrant and x=π+π6=7π6∴General solution is x=2nπ+7π6,n∈z

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