Question

help me with questions plz​

Answer 1

Given:-

tanθ = $\sf{\dfrac{12}{13}}$

To Find:-

The value of $\sf{\dfrac{13cos\theta - 12sin\theta}{13cos\theta + sin\theta}}$

Solution:-

We know,

tanθ = $\sf{\dfrac{Perpendicular}{Base}}$

Therefore,

$\sf{\dfrac{Perpendicular}{Base} = \dfrac{12}{13}}$

On comparing, We get,

Perpendicular = 12 units

Base = 13 units

According To Pythagoras Theorem,

$\sf{(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2}$

= $\sf{Hypotenuse = \sqrt{(13)^2 + (12)^2}}$

= $\sf{Hypotenuse = \sqrt{169 + 144}}$

= $\sf{Hypotenuse = \sqrt{313}}$

= $\sf{Hypotenuse = 17.7\:units}$

Now,

Cosθ = $\sf{\dfrac{Base}{Hypotenuse} = \dfrac{13}{17.7}}$

Sinθ = $\sf{\dfrac{Perpendicular}{Hypotenuse} = \dfrac{12}{17.7}}$

Now substituting the values in the equation,

$\sf{\dfrac{13cos\theta - 12sin\theta}{13cos\theta+12sin\theta}}$

= $\sf{\dfrac{13\times\dfrac{13}{17.7} - 12\times \dfrac{12}{17.7}}{13\times\dfrac{13}{17.7}+12\times\dfrac{12}{17.7}}}$

= $\sf{\dfrac{\dfrac{169}{17.7}-\dfrac{144}{17.7}}{\dfrac{169}{17.7}+\dfrac{144}{17.7}}}$

= $\sf{\dfrac{\dfrac{169-144}{17.7}}{\dfrac{169+144}{17.7}}}$

= $\sf{\dfrac{\dfrac{25}{17.7}}{\dfrac{313}{17.7}}}$

= $\sf{\dfrac{25}{17.7}\times\dfrac{17.7}{313}}$

= $\sf{\dfrac{25}{313}\:\:\:\:[Answer]}$

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Remember!!!

• Sinθ = Perpendicular/Hypotenuse

• Cosθ = Base/Hypotenuse

• Tanθ = Perpendicular/Base

• Cosecθ = Hypotenuse/Perpendicular

• Cosθ = Hypotenuse/Base

• Cotθ = Base/Perpendicular

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