A) 2
B) 1
C) 0
D) 3
E) 4
Correct Answer: A
Solution :
\[tan\text{ }x+sec\text{ }x=2\text{ }cos\text{ }x\] \[\Rightarrow \] \[1+sin\text{ }x=2-2\text{ }si{{n}^{2}}x\] \[\Rightarrow \] \[2\text{ }si{{n}^{2}}x+sin\text{ }x-1=0\] \[\Rightarrow \] \[2\text{ }si{{n}^{2}}x+2\text{ }sin\text{ }x-sin\text{ }x-1=0\] \[\Rightarrow \] \[(2\text{ }\sin x-1)(sin\text{ }x+1)=0\] \[\Rightarrow \] \[sin\text{ }x=-1,\frac{1}{2}.\] \[\therefore \]Number of solution in the interval \[(0,2\pi )=2\]
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