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The number of solutions of the equation ...

The number of solutions of the equation `3^(2sec^(2)x)+1=10.3^(tan^(2)x)` in the interval `[0,2pi]` is

A

8

B

6

C

3

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`3^(2(1+tan^(2)x))+1-10.3^(tan^(2)x)=0`
`rArr 3^(2)(3^(tan^(2)x))^(2)+1-10.3^(tan^(2)x)=0`
Put `3^(tan^(2)x)=t`
`9t^(2)-10t + 1=0`
`rArr t=(1)/(9)` and t = 1
`rArr 3^(tan^(2)x)=3^(-2)` and `3^(tan^(2)x)=1`
`rArr tan^(2)x=-2` gives no solution and `tan^(2)x=1` gives four solutions
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