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Question

General solution of the equation (31)sinθ+(3+1)cosθ=2 is

A
2nπ±π4+π12
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B
nπ+(1)nπ4+π12
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C
2nπ±π4π12
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D
nπ+(1)nπ4π12
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Solution

The correct option is A 2nπ±π4+π12
Let 3+1=rcosα and 31=rsinα

r2=(3+1)2+(31)2=8

and tanα=313+1=11/31+1/3=tan(π4π6)

=tan(π12)α=π12

From the given equation, we get rcos(θα)=2

cos(θπ12)=12=cosπ4

θπ12=2nπ±π4θ=2nπ±π4+π12

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