Question

If 7sinθ + 24cosθ = A sin (θ +Φ ) then what is A and Φ?

Answer 1

( 1+m/1−m)cotϕ

Step-by-step explanation:

steps are in with the attachment..

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Answer 2

Step-by-step explanation:

Solution :

Apply componendo and dividendo

cos(θ+ϕ) + cos(θ−ϕ) = m + 1

=> _____________________

cos(θ+ϕ) - cos(θ−ϕ) = m - 1

cos(θ+ϕ) + cos(θ−ϕ) = m + 1

=> _____________________

- cos(θ-ϕ) - cos(θ+ϕ) = m - 1

2cos(θ)⋅cos(ϕ) = 1 + m

=> ________________

2sin(θ)⋅sin(ϕ) = 1 - m

=> cotθ⋅cotϕ = 1 + m / 1 - m

=> tanθ = (1 - m / 1 + m).cotϕ