Question

if 3 sin theta+4 cos theta=5 then find value of 4 sin theta -3 cos theta​

Answer 1

Answer :

4sinθ - 3cosθ = 0

Solution :

• Given : 3sinθ + 4cosθ = 5
• To find : 4sinθ - 3cosθ = ?

We have ;

=> 3sinθ + 4cosθ = 5

=> sinθ•3 + cosθ•4 = 5

=> sinθ•(3/5) + cosθ•(4/5) = 1

=> sinθ•cos∅ + cosθ•sin∅ = 1

[ Where cos∅ = 3/5 and sin∅ = 4/5 ]

=> sin(θ+∅) = sin90°

=> θ + ∅ = 90°

Now ,

Taking cosine both the sides , we get ;

=> cos(θ+∅) = cos90°

=> cosθ•cos∅ - sinθ•sin∅ = 0

=> cosθ•(3/5) - sinθ•(4/5) = 0

=> cosθ•3 - sinθ•4 = 0

=> 3cosθ - 4sinθ = 0

=> -(-3cosθ + 4sinθ) = 0

=> -3cosθ + 4sinθ = 0

=> 4sinθ - 3cosθ = 0

Hence ,

4sinθ - 3cosθ = 0