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The number of distinct of real roots of the equation `tan^(2)2x+2tan2x tan3x-1=0` in the interval `[0,(pi)/(2)]` is

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The number of distinct of real roots of the equation `tan^(2)2x+2tan2x tan3x-1=0` in the interval `[0,(pi)/(2)]` is
A. 1
B. 2
C. 3
D. 4
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Correct Answer - C
tan 2x (tan 2x + tan 3x) = 1 - tan 2x tan 3x
`rArr tan 2x tan 5x =1`
`rArr cos 7x = 0`
`therefore x=(2k+1)(pi)/(14),k in Z`
`therefore x =(pi)/(14,(3pi)/(14),(5pi)/(14)`
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