Math, asked by Anonymous, 3 months ago

Please answer 11 question?

Class - 10th
Chapter - Trigonometry

I swear spammed answer ID report .

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Answers

Answered by Anonymous
9

Given:-

 \sqrt{3} sin \: x - cos \: x = 0

To find:-

Value of x

Solution:-

 \sqrt{3} sin \: x - cos \: x = 0

 =  >  \sqrt{3} sin \: x = cos \: x

 =  >  \sqrt{3} sin \: x =  \sqrt{1 -  {sin}^{2}x }

 =  >  { (\sqrt{3}sin \: x) }^{2}  = 1 -  {sin}^{2} x

 =  > 3 {sin}^{2}x = 1 -  {sin}^{2}  x

 =  > 4 {sin}^{2} x =  1

 =  >  {sin}^{2} x =  \frac{1}{4}

 =  > sin \: x =  \sqrt{ \frac{1}{4} }

 =  > sin \: x =  \frac{1}{2}

We know that,

sin 30° = 1/2 -(1)

but, sin x = 1/2 -(2)

From (1) and (2), we get,

x = 30°

Answered by SuitableBoy
44

{\huge{\underline{\underline{\bf{\maltese Question}}}}}

Q - If √3 sin x - cos x = 0 and 0°<x<90° , find the value of x .

{\huge{\underline{\underline{\bf{\maltese Answer\checkmark}}}}}

In this question ,

All we have to do is just Modifying the Given equation .

 \rm \:  \sqrt{3} \:  sin \: x - cos \: x = 0

 \rm \implies \:  \sqrt{3}  \: sin \: x = cos \: x

 \implies \:   \rm \: \dfrac{ \sqrt{3} \: sin \: x }{cos \: x}  = 1

 \implies \rm \:  \frac{sin \: x}{cos \: x}  =  \frac{1}{ \sqrt{3} }  \\

  \rm\implies \: tan \: x  =  \frac{1}{ \sqrt{3} }  \\

Now ,

Using the trigonometric table ,

 \rm \: tan \: x \:  =  \: tan \: 30 \degree

So , on comparing ,

   \pink\bigstar\boxed{ \rm \: x = 30 \degree}

___________

Know More :

  •  \sf \: tan \:  \theta =  \frac{sin \:  \theta}{cos \:  \theta}  \\
  •  \sf \: sec  \: \theta =  \frac{1}{cos \:  \theta}  \\
  •  \sf \: cosec \:  \theta =  \frac{1}{sin  \:  \theta}  \\
  •  \sf \:  {sin}^{2}  \: x +   {cos}^{2}  \: x = 1
  •  \sf \: 1 +  {cot}^{2}  \: x = {cosec}^{2}  \: x
  •  \sf \:  {tan}^{2}  \: x + 1 =  {sec}^{2}  \: x

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AestheticSky: Perfect and to the point !!
AestheticSky: very helpful ⭐⭐⭐
SuitableBoy: Thank You :)
AestheticSky: don't mention :)
SuitableBoy: Okay ツ
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