Question

If θ be acute angle and cosθ = 15/17, then the value of cot (90° - θ) is?? nhi yr nhi h hm ☺❤✌ always keep smiling ☺​

Answer 1

Given :

If θ be acute angle and cos θ = 15/17.

To find :

• The value of cot (90° - θ) is what ?

Solution :

• Cosθ = 15/17

METHOD : 1

According to the trigonometry identities

• cos²θ + sin²θ = 1

→ sin²θ = 1 - cos²θ

→ sinθ = √1 - cos²θ

• Put the value of cosθ

→ sinθ = √1 - (15/17)²

→ sinθ = √1 - 225/289

→ sinθ = √289 - 225/289

→ sinθ = √64/289

→ sinθ = 8/17

• Now the value of cot (90° - θ)

→ cot (90° - θ)

→ tanθ

→ sinθ/cosθ

• Substitute the values

→ 8/17/15/17

→ 8/17 × 17/15

→ 8/15

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• METHOD : 2

Solve this question by the Pythagoras theorem

★(hypotenuse)²=(base)²+ (perpendicular)²

• As we know that

→ cos θ = base/hypotenuse

→ cosθ = 15/17

Let the perpendicular be x , base be 15x and hypotenuse be 17x

• According to the theorem

→ (17x)² = (15x)² + (x)²

→ 289x² = 225x² + x²

→ x² = 289x² - 225x²

→ x² = 64x²

→ x = √64x² = 8x

• Now the value of cot (90° - θ)

→ cot (90° - θ)

→ tanθ

→ perpendicular/base

→ 8x/15x

→ 8/15

•°• The value of cot (90° - θ) is 8/15

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Answer 2

Given:-

• θ is an acute angle

• cos θ = $\dfrac{15}{17}$

To Find:-

• Value of cot (90° - θ)

Solution:-

As Given,

cos θ = $\dfrac{15}{17}$ ____{1}

And as we know,

$⟹\:cos \:θ = \dfrac{Base}{Hypotenuse}$____{2}

From {1} and {2},

$⟹\:\dfrac{15}{17}= \dfrac{Base}{Hypotenuse}$

So,

• Base = 15

• Height = 17

Using Pythagoras theorem,

${\boxed{Hypotenuse² = Perpendicular ² + Base²}}$

$⟹\: (17)² = Perpendicular² + (15)²$

$⟹ \:Perpendicular² = 289 - 225$

$⟹ \:Perpendicular = \sqrt{64}$

$⟹ \:Perpendicular = 8$

$⟹\:cot\:(90-θ)=tan\:θ$ ____{3}

As we know,

$⟹ \:tan\: θ = \dfrac{Perpendicular}{Base}$

$⟹\:tan\: θ = \dfrac{8}{15}$

From {3},

$⟹\:cot \:(90° - θ) = \dfrac{8}{15}$

Hence, the value of cot (90° - θ) is ${\bold{{\dfrac{8}{15}.}}}$

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