General solution of simultaneous equations tanθ=−13 and cosθ=32 is

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θ=nπ+π6,n∈z

θ=nπ+11π6,n∈z

θ=2nπ+π3,n∈z

θ=2nπ+11π6,n∈z

answer is D.

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Detailed Solution

We have tanθ=−13<0,cosθ=32>0∴θbelongs to 4th quadrant and it is 2π−π6=11π6∴general solution is θ=2nπ+11π6,n∈z

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