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Radda [10]
2 years ago
10

Solve the following surd given below (1-√5)÷(1+√5)​

Mathematics
1 answer:
Shkiper50 [21]2 years ago
4 0

\dfrac{1-\sqrt 5}{1+\sqrt 5}\\\\\\=\dfrac{\left( 1- \sqrt 5\right)\left( 1- \sqrt 5\right)}{\left( 1+ \sqrt 5\right)\left( 1- \sqrt 5\right)}\\\\\\=\dfrac{\left( 1-\sqrt 5)^2}{1^2 - \left(\sqrt 5 \right)^2}\\\\\\=\dfrac{1+\left(\sqrt 5 \right)^2 -2 \sqrt 5\cdot 1}{1-5}\\\\\\=\dfrac{1+5-2\sqrt 5}{-4}\\\\\\=-\dfrac{6-2\sqrt 5}{4}\\\\\\=-\dfrac{2\left(3-\sqrt 5 \right)}{4}\\\\\\=-\dfrac{3-\sqrt 5}{ 2}\\\\\\=\dfrac{\sqrt 5 -3}{2}

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PLEASE HELP ME I'M GIVING 20PTS AND MARKING BRAINLIEST!!!!
pishuonlain [190]

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

  • \cos{\theta} = \pm \frac{2\sqrt{2}}{3}
  • \tan{\theta} = \pm \frac{\sqrt{2}}{4}

<h3>What is the trigonometric identity using in this problem?</h3>

The identity that relates the sine squared and the cosine squared of the angle, as follows:

\sin^{2}{\theta} + \cos^{2}{\theta} = 1

In this problem, we have that the sine is given by:

\sin{\theta} = \frac{1}{3}

Hence, applying the identity, the cosine is given as follows:

\cos^2{\theta} = 1 - \sin^2{\theta}

\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2

\cos^2{\theta} = 1 - \frac{1}{9}

\cos^2{\theta} = \frac{8}{9}

\cos{\theta} = \pm \sqrt{\frac{8}{9}}

\cos{\theta} = \pm \frac{2\sqrt{2}}{3}

The tangent is given by the sine divided by the cosine, hence:

\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}

\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}

\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}

\tan{\theta} = \pm \frac{\sqrt{2}}{4}

More can be learned about trigonometric identities at brainly.com/question/24496175

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5 0
2 years ago
I need help with this
9966 [12]

Answer:

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3 years ago
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3 years ago
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Factorize x²-3x-28 ===> (x-7)(x+4)

4x + 12 can be written====> 4(x+3)

Then the question could be written as follows:

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