contestada

Examine the following steps. Which do you think you might use to prove the identity Check all that apply. Write tan(x y) as sin (x y) over cos(x y). Use the sum identity for sine to rewrite the numerator. Use the sum identity for cosine to rewrite the denominator. Divide both numerator and denominator by cos(x)cos(y). Simplify fractions by dividing out common factors or using the tangent quotient identity.

Respuesta :

The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

According to the statement

we have given that the a identity and we have to use in the given conditions.

So, For this purpose, we know that the

Given that the required identity of Tangent is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)),

we have:

tan(x + y) = sin(x + y)/(cos(x + y))

sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

After solving this identity according to the statement it is clear that all the options are correct.

So, The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

Learn more about Tangent here

https://brainly.com/question/4470346

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Examine the following steps. Which do you think you might use to prove the identity Tangent (x) = StartFraction tangent (x) + tangent (y) Over 1 minus tangent (x) tangent (y) EndFraction question mark

Check all that apply.

-Write tan(x + y) as sin (x + y) over cos(x +y).

-Use the sum identity for sine to rewrite the numerator.

-Use the sum identity for cosine to rewrite the denominator.

-Divide both numerator and denominator by cos(x)cos(y).

-Simplify fractions by dividing out common factors or using the tangent quotient identity.

#SPJ4

Otras preguntas