Math 1022 Test 3

Which of the following is not a variation of a Pythagorean​ Identity?

1-cot^2(theta) = csc^2(theta)

Which of the following is​ true?

A trigonometric identity is valid for all values of the independent variable for which both sides of the identity are defined.

Which of the following is not a process commonly used to verify an​ identity?

If more than one term appears in the denominator of an​ expression, try using long division to simplify the expression.

If (alpha/2) is an angle with a terminal side lying in Quadrant​ IV, then which of the following expressions is not equivalent to tan(alpha/2)?

SQR 1-cos(alpha)/1+cos(alpha)

Which of the following is the correct sum formula for the cosine​ function?

cos(α+β)=cosαcosβ−sinαsinβ

Which of the following is not a valid​ double-angle formula for​ cosine?

cos2θ=2sin2θ−1

Which of the following is not a valid property of trigonometric​ functions?

cot(-theta) = cot(theta)

Which of the following can best be evaluated using the sum formula for the sine​ function?

sin(tan^-1 1+cos^-1 SQR(3)/2)

Which of the following is the correct difference formula for the sine​ function?

sin(α−β)=sinαcosβ−cosαsinβ

Which of the following is the correct sum formula for the tangent​ function?

tan(α+β)= (tanα+tanβ)/(1−tanαtanβ)

Which of the following is the correct difference formula for the tangent​ function?

tan(α−β)= (tanα−tanβ)/(1+tanαtanβ)

Using the technique of changing to sines and cosines to verify an​ identity, determine which of the following is not an identity.

(sin(theta)csc(theta))/cos^2(theta) = tan^2(theta)

If (a/2) is an angle with a terminal side lying in Quadrant​ III, then which of the following expressions is equivalent to sin(a/2)?

-SQR 1-cos(alpha)/2