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kykrilka [37]
3 years ago
7

Look at the triangle show on the right. The Pythagorean Theorem states that the sum of the squares of the legs of a right triang

le is equal to the square of the hypotenuse. Margaret uses this theorem to simplify and rewrite the expression (b/r)^2 + (a/r)^2 using the triangle shown. Which trigonometric identity can she prove with her expression? *
Mathematics
1 answer:
Vladimir [108]3 years ago
3 0

Answer:

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

Step-by-step explanation:

Given

(\frac{b}{r})^2  + (\frac{a}{r})^2

Required

Use the expression to prove a trigonometry identity

The given expression is not complete until it is written as:

(\frac{b}{r})^2  + (\frac{a}{r})^2  = (\frac{r}{r})^2

Going by the Pythagoras theorem, we can assume the following.

  • a = Opposite
  • b = Adjacent
  • r = Hypothenuse

So, we have:

Sin\theta = \frac{a}{r}

Cos\theta = \frac{b}{r}

Having said that:

The expression can be further simplified as:

(\frac{b}{r})^2  + (\frac{a}{r})^2  = 1

Substitute values for sin and cos

(\frac{b}{r})^2  + (\frac{a}{r})^2  = 1 becomes

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

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