Question

If 3tanA=1 prove that 3sinA=cosA​

Answer 1

$\huge{\underline{\sf{Solution:-}}}$

1 + Sin²A = 3SinA Cos A

Cos²A + Sin²A + Sin²A = 3SinA CosA [ 1 = Sin² +bCos A]

Cos²A + 2Sin²A = 3SinA CosA → (1)

Divide eq (1) by cos²A we get,

1 + 2Tan²A = 3 TanA

1 + 2Tan²A - 3 TanA = 0

(2TanA - 1) ( TanA - 1) = 0

2TanA - 1 = 0 × TanA - 1 = 0

2TanA = 1 × TanA = 1

TanA = 1/2 × TanA = 1

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Answer 2

Step-by-step explanation:

$3tan(a) = 1 \\ 3 \times \sin(a) \div \cos(a) = 1 \\ 3 \sin(a) = \cos(a) \\ \\ \: \: \: \: \: \: \: hence \: proved$

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