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If 7sin^2theta+3cos^2theta=4, Find the v...

If `7sin^2theta+3cos^2theta=4,` Find the value of `tantheta`

A

`1/(sqrt(2))`

B

`1/(sqrt(3))`

C

1

D

`2/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
B
`7 sin ^(2) theta + 3 cos ^(2) theta =4`
`implies 4 sin ^(2) theta + 3 sin ^(2) theta + 3 cos ^(2) theta =4`
`implies 4 sin ^(2) theta + 3 (sin ^(2) theta + cos ^(2) theta )=4`
`implies 4 sin ^(2) theta + 3 xx1=4[:' sin ^(2) theta + cos^(2)theta =1]`
`implies 4sin ^(2) theta = 1 implies sin ^(2)theta =(1) /(4) .`
`therefore cos^(2)theta =(1-sin ^(2) theta)=(1-(1)/(4))=(3)/(4).`
`therefore tan^(2)theta =(sin ^(2) theta)/( cos ^(2) theta)=((1)/(4)xx(4)/(3))=(1)/(3).`
hence , `tan theta =(1)/(sqrt(3)).`
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