If 3sin theta-2cos theta=3 then, 2sin theta+3cos theta= ? 【theta getter than 0】
Answers
Formulas to Use :
( a - b )² = a² + b² - 2 ab
See the table in attachment for values .
Find theta
3 sin θ - 2 cos θ = 3
= > 3 sin θ - 3 = 2 cos θ
Squaring both sides we get :
= > ( 3 sin θ - 3 )² = 4 cos² θ
= > 9 sin² θ + 9 - 18 sin θ = 4 ( 1 - sin² θ )
= > 9 sin² θ + 9 - 18 sin θ = 4 - 4 sin² θ
= > 9 sin² θ + 4 sin² θ - 18 sin θ + 9 - 4 = 0
= > 13 sin² θ - 18 sin θ + 5 = 0
= > 13 sin² θ - 13 sin θ - 5 sin θ + 5 = 0
= > 13 sin θ ( sin θ - 1 ) - 5 ( sin θ - 1 ) = 0
= > ( 13 sin θ - 5 )( sin θ - 1 ) = 0
Either
= > sin θ - 1 = 0
= > sin θ = 1
Or :
= > 13 sin θ - 5 = 0
= > 13 sin θ = 5
= > sin θ = 5 / 13
Neglect the value of fraction :
sin θ = 1
For an acute angle :
= > sin θ = sin 90°
= > θ = 90°
Find the value of the given expression :
2 sin θ + 3 cos θ
= > 2 sin 90° + 3 cos 90°
= > 2 ( 1 ) + 3 ( 0 )
= > 2 + 0
= > 2
ANSWER :
The value would be 2
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