Question

In right triangle abc, when angles a and b add up to 90 degrees, what is the cosine of b equal to

Answer 1

Answer:

cos B = sin A

Step-by-step explanation:

Given: Δ ABC is a right angles triangle

           m∠A + m∠B = 90°

To find: Cos B equals to

Figure is attached.

Using trigonometric ratios in Δ ABC,

We get,

$cos\,B\,=\,\frac{base}{hypotenuse}\,=\,\frac{CB}{AB}$

$sin\,B\,=\,\frac{altitude}{hypotenuse}\,=\,\frac{AC}{AB}$

$cos\,A\,=\,\frac{altitude}{hypotenuse}\,=\,\frac{AC}{AB}$

$sin\,B\,=\,\frac{base}{hypotenuse}\,=\,\frac{CB}{AB}$

So, From above it is clear

cos B = sin A

Therefore, cos B = sin A

Answer 2

In that case, cosine of b = sine of a.