If 5 sin + 3 cos 0 = 4, find the value of
3 sino - 5 coso.
Answers
Answered by
0
Answer:
Consider the given equation.
5sinθ+3cosθ=4 …… (1)
On squaring both sides, we get
25sin
2
θ+9cos
2
θ+30sinθcosθ=16
16sin
2
θ+9(sin
2
θ+cos
2
θ)+30sinθcosθ=16
16sin
2
θ+30sinθcosθ=16−9=7 ……. (2)
Suppose that,
3sinθ−5cosθ=p
On squaring both sides, we get
9sin
2
θ+25cos
2
θ−30sinθcosθ=p
2
……. (3)
On adding equation (2) and (3), we get
9sin
2
θ+25cos
2
θ+16sin
2
θ=7+p
2
25sin
2
θ+25cos
2
θ=7+p
2
7+p
2
=25(sin
2
θ+cos
2
θ)
p
2
=25−7
p
2
=18
p=±3
2
Hence, the value of 3sinθ−5cosθ is ±3
2
Answered by
0
Answer:
consider the given equation 5 sin + 3 coso=4 (1) on squaring both sides we get 25 sin ^2 theta + 4 cos ^ theta + 30 on sin
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