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If sinA+cosA=0 and A lies in 4th quadran...

If `sinA+cosA=0` and A lies in 4th quadrant, find the values of `sinA` and `cosA.`

Text Solution

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`sinA+cosA=0`
`rArr sinA=-cosA`
`rArr (sinA)/(cosA)=-1`
`rArr sec^(2)A=1+tan^(2)A`
`=1+(-1)^(2)=2`
secA`=sqrt(2)`,
(sec is positive in 4th quadrant)
`rArr cosA=1/(secA)=1/sqrt(12)` Ans.
`rArr cosA=1/(secA)=1/sqrt(2)`.
and `sinA=(sinA)/(cosA). cosA=tanA.cosA`
`=(-1).1/sqrt(2)=-1/sqrt(2)` Ans. and sinA`=(sinA)/(cosA).cosA=tanA. cosA`
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