Question

In a APQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1 then the acute angle 'R' is equal to​

Answer 1

Answer:

Given trignometric equations are:

3sinP+4cosQ=6 -------(1)

4sinQ+3cosP=1 -------(2)

Squaring both equations (1) and (2) and adding them, we get

⇒9(sin2P+cos2P)+16(sin2Q+cos2Q)+24(sinQcosP+cosQsinP)=36+1

⇒9+16+24sin(P+Q)=37

∴sin(P+Q)=2437−25=2412=21

∴P+Q=30°

Hence, angle R=180°−30°=150°=65πradian

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