Question

Given that sinƟ=a/b ,then tanƟ is equal to (a) √2+ 2 (b) √ 2−2 (c) √2− 2 (d) √ 2−2​

Answer 1

Given : Sinθ = a/b

To Find :  Tanθ

1.  $\dfrac{b}{ \sqrt{a^2+b^2} }$

2. $\dfrac{b}{ \sqrt{b^2-a^2} }$

3. $\dfrac{a}{ \sqrt{a^2+b^2} }$

4. $\dfrac{a}{ \sqrt{b^2-a^2} }$

Solution:

Sinθ = a/b

Sinθ = Perpendicular / Hypotenuse

Perpendicular = a

Hypotenuse =  b

Pythagorean theorem: square on the hypotenuse of a right-angled triangle is  equal to the sum of the squares of the other two perpendicular sides.

Hypotenuse² = base² + Perpendicular²

b² = base²  + a²

=> base² = b² - a²

=> base = √b² - a²

tanθ = Perpendicular / Base

=> tanθ =  a/√b² - a²

tanθ =   $\dfrac{a}{ \sqrt{b^2-a^2} }$

Correct option is d) $\dfrac{a}{ \sqrt{b^2-a^2} }$

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