Question

9 sin theta + 40 cos theta equals to 41 prove that 41 cos theta = 40

Answer 1

Answer:

9sinθ + 40cosθ = 41

⇒9sinθ/sinθ + 40cosθ/cosθ = 41/cosθ

⇒9 + 40tanθ = 41secθ

⇒(9 + 40tanθ)² = (41secθ)²

⇒9² + 40²tan²θ + 2(9)(40)tanθ = 41²sec²θ

⇒81 + 1600tan²θ + 720tanθ = 1681 + 1681tan²θ

⇒81tan²θ - 720tanθ + 1600 = 0

⇒(9tanθ)² - 2(9tanθ)(40) + 40² = 0

⇒(9tanθ - 40)² = 0

⇒tanθ = 40/9

so, sinθ = 40/41 ,

cosecθ = 41/40,

cosθ = 9/41 ,

secθ = 41/9,

cotθ = 9/40