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If tantheta=3 and theta lies in third qu...

If `tantheta=3` and `theta` lies in third quadrant then `sintheta=`

A

`(1)/(sqrt(10))`

B

`-(1)/(sqrt(10))`

C

`(-3)/(sqrt(10))`

D

`(3)/(sqrt(10))`

Text Solution

Verified by Experts

The correct Answer is:
C
Given that, `" "tantheta=3`
`rArr" "sec^(2)theta=1+tan^(2)theta`
`rArr" "sectheta=sqrt(1+9)=pmsqrt(10)`
`rArr" "sectheta=-sqrt(10)`
` rArr" "costheta=-(1)/(sqrt(10))`
`rArr" "sintheta=pmsqrt(1-(1)/(10))=pmsqrt((9)/(10))=pm(3)/(sqrt(10))" "` [since, `theta` lines in third quadrant]
` therefore" "sintheta=-(3)/(sqrt(10))`
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