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katrin2010 [14]
2 years ago
12

use compound angle formulae to find sin 15 and cos 15 in form of [ surd a (surd b + c) ] . Hence, find tan 15 in the simplest su

rd form​
Mathematics
1 answer:
inysia [295]2 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Using the difference formulae for sine and cosine

sin(x - y) = sinxcosy - cosxsiny

cos(x - y) = cosxcosy + sinxsiny

sin15° = sin(45 - 30)°

sin(45 - 30)°

= sin45°cos30° - cos45°sin30°

= \frac{\sqrt{2} }{2} × \frac{\sqrt{3} }{2} - \frac{\sqrt{2} }{2} × \frac{1}{2}

= \frac{\sqrt{6} }{4} - \frac{\sqrt{2} }{4}

= \frac{\sqrt{6}-\sqrt{2}  }{4}

----------------------------------------------------------------------------------

cos15° = cos(45 - 30)°

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= \frac{\sqrt{2} }{2} × \frac{\sqrt{3} }{2} + \frac{\sqrt{2} }{2} × \frac{1}{2}

= \frac{\sqrt{6} }{4} + \frac{\sqrt{2} }{4}

= \frac{\sqrt{6}+\sqrt{2}  }{4}

-------------------------------------------------------------------------------------

tan15° = \frac{sin15}{cos15}

= \frac{\sqrt{6}-\sqrt{2}  }{4} × \frac{4}{\sqrt{6}+\sqrt{2}  }

= \frac{\sqrt{6}-\sqrt{2}  }{\sqrt{6}+\sqrt{2}  }

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator, that is (\sqrt{6} - \sqrt{2} )

= \frac{(\sqrt{6}-\sqrt{2})^2  }{(\sqrt{6}+\sqrt{2})(\sqrt{6}-\sqrt{2})    }

= \frac{6-4\sqrt{3}+2 }{6-2}

= \frac{8-4\sqrt{3} }{4}

= 2 - \sqrt{3}

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melamori03 [73]

Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC, Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1), Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.

Given: The diagram is given and we need to find the errors and then fix them. Also ΔTSR ≈ ΔTCD

Let's solve the given question:

Given that ΔTSR ≈ ΔTCD

So we know by the properties of the similarity that if two triangles are similar then the ratio of their corresponding sides is equal.

So, ΔTSR ≈ ΔTCD

=> RT / TD = ST / TC

=> 14 / 7 = 16 / (x - 1)

In the question, we can observe that the given side ratio is DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC.

The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).

The third error is the value of x.

We can find the correct value of x from the given equation:

14 / 7 = 16 / (x - 1)

=> 2 = 16 / (x - 1)

Multiplying both sides by (x - 1):

(x - 1) × 2 = 16 / (x - 1) × (x - 1)

=> 2(x - 1) = 16

Multiplying both sides by 1 / 2:

2(x - 1) × 1 / 2= 16 × 1 / 2

=> x - 1 = 8

Adding 1 on both sides:

x - 1 + 1 = 8 + 1

x = 9

Therefore x = 9.

Hence the errors are:

Error 1: DT / TS × CT / TR which is the first error. We can fix the error by writing the correct equation RT / TD = ST / TC

Error 2: The second error is 7 / 16 × (x - 1) / 14 and we can fix the error by writing the equation 14 / 7 = 16 / (x - 1).

Error 3:The third error is the value of x and we can find the correct value of x from the equation 14 / 7 = 16 / (x - 1) and the value of x is 9.

Know more about "similar triangles" here: brainly.com/question/14366937

#SPJ9

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1 year ago
Bryan, Angela, Elan, and Fiona folded some paper flowers for their school fund-raising project. Elan folded one-fifth of the pap
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Answer:

a) 88

b) 162 $

Step-by-step explanation:

Given Bryan sold 9 more flowers than Elan

1/4 x - 1/5 x = 9

x/20 = 9

x = 180

Flowers with Bryan = 45

Flowers with Elan = 36

45+36 = 81

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Flowers with Fiona = 8/9 * 99 = 88

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3 years ago
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Answer:

yes all are right

Step-by-step explanation:

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2 years ago
With similar triangles, the ratios of all three pairs of corresponding sides are equal
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<h3>Yes, this is true.</h3>

To be considered similar triangles, the angles must be the exact same, and the sides must be proportional. The side lengths do not have to be exactly the same, but they must be proportional (like a ratio, suppose one triangle has a side length of 1, and the similar triangle has a side length of 3. The ratio is 1:3, and all sides will follow this ratio.)

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Answer:

Step-by-step explanation:

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This angle is vertical with angle z, so angle z also equals 99°

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