Question

if 3tan A=4.then find sin A and cos A​

Answer 1

Given :

3tanA = 4

To find :

• sinA
• cosA

Solution :

We know that

• tanA = Perpendicular ÷ Base

• sinA = Perpendicular ÷ Hypoteneus

• cosA = Base ÷ Hypoteneus

Now we are given that,

$\sf \: 3 \tan(A) = 4 \\ \\ \sf \implies \: \tan(A)\: = \: \dfrac{4}{3} \\ \\ \sf \implies \: \dfrac{P}{B} \: = \dfrac{4}{3}$

Now , let P = 4 than B = 3

By using Pythagoras theorem in ∆LMN, we get;

H² = P² + B²

➝ H² = 4² + 3²

➝ H² = 16 + 9

➝ H² = 25

➝ H = √25

➝ H = +5 { as side can't be negative }

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Now

sinA = Perpendicular ÷ Hypoteneus

➝ sinA = P/H

➝ sinA = 4/5

cosA = Base ÷ Hypoteneus

➝ cosA = B/H

➝ cosA = 3/5

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ANSWER :

• sinA = 4/5
• cosA = 3/5