1.

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))`

Answer» Correct Answer - 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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