1.

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`

Answer» `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`
`(P+Q) = pi/6 or 5 pi/6 `
`R = pi - (P+Q) = pi/6`
as `5pi/6` not possible
option 1 is correct


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