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

Options

A. `( 5pi)/(6)`
B. `(pi)/(6)`
C. `(pi)/(4)`
D. `(3pi)/(4)`

Answer

B

Explanation

`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)`