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If sinA=-4/5 and A lies in 3rd quadrant,...

If `sinA=-4/5` and A lies in 3rd quadrant, find the values of (i) `sin2A` ii) `cos2A`.

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`sinA=-4/5` (A lies in 3rd quadrant)
`therefore cos^(2)=1-sin^(2)A`
`=1-(4/5)^(2)=1-16/15=9/25`
`rArr cosA=-3/5` `(therefore` A lies in 3rd quadrant)
i) sin2A=2sinAcosA
`=2(-4/5)(-3/5)=24/25`
ii) `cos2A=1-2sin^(2)A=1-2(-4/5)^(2)`
`=1-32/25=-7/25`.Ans
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