3SinA+4CosA = BSin(C+A) isme A ka man kya hoga plzz give me solution
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In triangle ABC, we are given that 3sinA+4cosB=6 and 4sinB+3cosA=1. Then the measure of the angle C is.
October 15, 2019
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Avdinesh Priya
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ANSWER
3sinA+4cosB=6....(i)
4sinB+3cosA=1....(ii)
squaring and adding (i) and (ii)
(9sin
2
A+16cos
2
B+24sinAcosB)+(16sin
2
B+9cos
2
A+24sinBcosA)=37
9(sin
2
A+cos
2
A)+16(sin
2
B+cos
2
B)+24(sinAcosB+sinBcosA)=37
25+24sin(A+B)=37
24sin(A+B)=12
sin(A+B)=
24
12
=
2
1
As A+B+C=π
A+B=π−C
sin(π−C)=
2
1
π−C=
6
π
⇒C=
6
5π
=150
o
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