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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±π4+(1)nπ12
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C
nπ±π4π12
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D
nπ±π4(1)nπ12
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Solution

The correct option is A 2nπ±π4+π12
The given equation is
(31)sinθ+(31)cosθ=2
Let (31)=rsinα;(31)=rcosα
r=(31)2+(3+1)2=22
and tanα=313+1=tan15o
α=15o=π12
Therefore, rsinαsinθ+rcosθcosα=2
22cos(θα)=2
θπ12=2nπ±π4
θ=2nπ±π4+π12

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