Question

Evaluate sin40° / cos41°​

Answer 1

Answer:

It is given that 9sinθ + 40cosθ = 41

Then we have to find all the trigonometric ratios

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

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