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In a PQR, if 3 P+4 Q=6 and 4 Q+3 P=1, then the angle {R} is e

Question

In a $Δ PQR$ , if $3 sin P + 4 cos Q = 6$ and $4 sin Q + 3 cos P = 1$ , then the angle $R$ is equal to:

\frac{5 π}{6}

\frac{π}{6}

\frac{π}{4}

\frac{3 π}{4}

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Liam Discussed

In a

Δ PQR

, if

3 sin P + 4 cos Q = 6

and

4 sin Q + 3 cos P = 1

, then the angle

R

is equal to:

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Consider,

3 sin P + 4 cos Q = 6

....(i)

4 sin Q + 3 cos P = 1

....(ii)

From (i) and (ii), we get

(3 sin P + 4 cos Q)^{2} + (4 sin Q + 3 cos P)^{2} = 37

\Rightarrow 24 sin (P + Q) = 12

\Rightarrow sin (P + Q) = \frac{1}{2}

\Rightarrow P + Q = \frac{5 π}{6}

\Rightarrow R = \frac{π}{6}

Hence, option 'B' is correct.

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Question Text	In a $Δ PQR$ , if $3 sin P + 4 cos Q = 6$ and $4 sin Q + 3 cos P = 1$ , then the angle $R$ is equal to:
Answer Type	Text solution:1
Upvotes	150