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In a DeltaP Q R , if 3""s in""P""+""4""c...

In a `DeltaP Q R` , if `3""s in""P""+""4""cos""Q""=""6` and `4""s in""Q""+""3""cos""P""=""1` , then the angle R is equal to (1) `(5pi)/6` (2) `pi/6` (3) `pi/4` (4) `(3pi)/4`

Text Solution

Verified by Experts

`P + Q+R = pi`
`3 sin P + 4 cos Q =6 (i) ; 4 sin Q + 3 cos P= 1 (ii)`
`R < pi/2`
eqn `(i)^2 + (ii)^2:`
`9sin^2 P + 24sinPcos Q + 16cos^2 Q+ 16sin^2 Q+ 24sin QcosP + 9cos^2 P= 36 +1 `
`9 + 16 + 24 (sin Pcos Q + cos P sin Q) = 37`
`25 + 24 (sin(P+Q))= 37`
`sin(P +Q) = (37-25)/24= 1/2`
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