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In a DeltaPQR. if 3 sinP +4 cosQ=6 and 4...

In a `DeltaPQR`. if `3 sinP +4 cosQ=6` and `4sinQ+3cosP=1`, then the angle `R` is equal to:

A

`( 5pi)/(6)`

B

`(pi)/(6)`

C

`(pi)/(4)`

D

`(3pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
`3 sin P + 4 cos Q =6" " `(i)
`4 sin Q + 3 cos P =1" " `(ii)
Squaring and adding (i) and (ii) we get ` sin (P+Q) = (1)/(2)`
`rArr P + Q = (pi)/(6) or (5pi)/(6)`
`rArr R =(5pi)/(6) or (pi)/(6)`
If `R = (5pi)` then `0 lt P, Q lt (pi)/(6)`
`rArr cos Q lt 1 and sin P lt (1)/(2)`
`rArr 3 sin P + 4 cos Q lt (11)/(2)`, which is not possible
So `R= (pi)/(6)`
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