Q. 504.6( 9 Votes )
If 4 cos θ + 3 si
Answer :
Given : 4 cos θ+ 3 sin θ = 5
Squaring both the sides, we get
⇒ (4 cos θ+ 3 sin θ)2 = 25
⇒ 16 cos2 θ + 9 sin2 θ + 2(4cos θ)(3sin θ)= 25 [∵ (a + b)2 =a2 +b2 +2ab]
⇒ 16 cos2 θ + 9 sin2 θ + 24 cosθ sinθ = 25
Divide by cos2 θ, we get
⇒ 16 + 9tan2 θ + 24 tanθ = 25sec2 θ
⇒ 16 + 9tan2 θ + 24 tanθ = 25(1 + tan2 θ) [∵ 1+ tan2θ = sec2 θ]
⇒ 16 + 9tan2 θ + 24 tanθ = 25+ 25 tan2 θ
⇒ 16tan2 θ – 24tanθ + 9 = 0
⇒ 16tan2 θ – 12 tanθ – 12 tanθ +9 = 0
⇒ 4tanθ (4tan θ – 3) – 3(4tan θ – 3) = 0
⇒ (4tan θ – 3)2 = 0
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