Question

Solve 4cos(x+50^(@))-sin(x-40^(@))=0 in the range x in 0 90^(@)). Give your answer in degrees.​

Answer 1

we have to solve 4cos(x + 50°) - sin(x - 40°) = 0 in the range of x ∈ [0° , 90°].

solution : 4cos(x + 50°) - sin(x - 40°) = 0

⇒4co[(x - 40°) + 90°] - sin(x - 40°) = 0

let x - 40° = A

⇒4cos(A + 90°) - sinA = 0

we know, cos(90° + θ) = -sinθ

⇒-4sinA - sinA = 0

⇒-5sinA = 0

⇒sinA = 0

⇒A = nπ , where n belongs to all integers

⇒(x - 40°) = nπ

for 0° < x < 90°

we should take n = 0

⇒x - 40° = 0

⇒x = 40°

Therefore the value of x is 40°.

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