Number of solutions of tanx=sinx, where x∈[−3π,3π]
A
No solution
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B
3
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C
Infinitely many
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D
7
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Solution
The correct option is D 7 Given: tanx=sinx
Solutions of equation tanx=sinx are same as the number of points of intersections of graphs of y=tanx and y=sinx
The graph is given below
it is obvious from the graph that tanx=sinx where tanx=sinx=0
And we know tanx=0⇔x=nπ,∀n∈Z
In the interval [−3π,3π], required solutions are x=−3π,−2π,−π,0,π,2π,3π
Hence number of solutions is 7.