Number of distinct solutions of secθ+tanθ=3,0≤θ≤3π , is
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a
2
b
5
c
4
d
3
answer is A.
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Detailed Solution
1+sinθcosθ=3sin2θ2+cos2θ2+2sinθ2cosθ2cos2θ2-sin2θ2=3cosθ2+sinθ22cosθ2-sinθ2cosθ2+sinθ2=3cosθ2+sinθ2cosθ2-sinθ2=31+tanθ21-tanθ2=3tanπ4+θ2=3g sol π4+θ2=nπ+π3θ=2nπ+2π3-π2n=0 θ=π6n=1 θ=2π+π6 two values