Question

if 9 sin theta +40 cos theta = 41, prove that 41 cos theta =40

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Question :-

if 9 sin theta +40 cos theta = 41, prove that 41 cos theta =40

solutions:-

it is given that 9sinθ + 40cosθ = 41

then we have to find all the trigonometric ratios

9sinθ + 40cosθ = 41

to find :-

⇒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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