Question

sinA= a/b find the value of tanA​

Answer 1

GIVEN :

$\sin(A) = \frac{a}{b}$

TO FIND :

$the \: value \: of \: \tan(A)$

FORMULA USED :

$\sin(θ) = \frac{perpendicular \: or \: height}{hypotenuse}$

$\tan(θ) = \frac{perpendicular \: or \: height}{base}$

or

$\tan(θ) = \frac{ \sin(θ) }{ \cos(θ) }$

$base = \sqrt{ {(hypotenuse)}^{2} - {(height)}^{2} }$

SOLUTION :

It is given that :-

$⟹SinA = \frac{a}{b}$

Now , we know :-

$\sin(θ) = \frac{perpendicular \: or \: height}{hypotenuse}$

Therefore ,

• a = height/ perpendicular
• b = hypotenuse

Now we have to find base :-

$⟹base \: = \sqrt{ {(hypotenuse)}^{2} - {(height)}^{2} }$

$⟹base = \sqrt{ {b}^{2} - {a}^{2} }$

Now we know :-

$⟹\tan(θ) = \frac{perpendicular \: or \: height}{base}$

$⟹tan(A) = \frac{a}{ \sqrt{ {b}^{2} - {a}^{2} }}$

ANSWER :

$tan(A) = \frac{a}{ \sqrt{ {b}^{2} - {a}^{2} }}$

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Learn more :-

1. Cosθ = base / hypotenuse

2. cossecθ = 1/ sinθ

3. sec θ = 1/cosθ

4. Cotθ = 1/ tanθ

5. Sin²θ+ Cos²θ= 1

6. Sec²θ - tan²θ = 1

7. cosec ²θ - cot²θ = 1

8. sin(90°−θ) = cos θ

9. cos(90°−θ) = sin θ

10. tan(90°−θ) = cot θ

11. cot(90°−θ) = tan θ

12. sec(90°−θ) = cosec θ

13. cosec(90°−θ) = sec θ

14. Sin2θ = 2 sinθ cosθ

15. cos2θ = Cos²θ- Sin²θ

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