In a  ΔPQR, if 3sin⁡P+4cos⁡Q=16 and 4sin⁡Q+3cos⁡P=1, Then the  angle R is equal to

Squaring and adding the given relations we get16+9+24sin⁡(P+Q)=37⇒sin⁡(P+Q)=1/2⇒sin⁡R=1/2⇒R=π/6   or 5π/6If R=5π/6, then P<π/6⇒3sin⁡P<3/2.⇒3sin⁡P+4cos⁡Q<3/2+4<6So R≠5π/6