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Problem: 13 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

Step 2Write the right side in terms of sine and cosine. Use the identities

Step 3Simplify.

Step 4Use the quotient identity

tanA = tanA

The identity is verified.

Problem: 15 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

Step 2Split the right side into two fractions.

Step 3Use the identities

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The identity is verified.

Problem: 17 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

secxcscx? tanx+ cotx

Step 2Write the right side in terms of sine and cosine. Use the identities

Step 3Find a common denominator.

Step 4Use the identity sin2x+ cos2x= 1.

Step 5

Write the right side as a product.

Step 6Use the identities

The identity is verified.

Problem: 19 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

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Step 2Split the right side into two fractions.

Step 3Write the fraction as a product.

Step 4Use the identities

Step 5Replace 1 by sin2A + cos2A.

(sinA + cosA)2 ? 2sinA cosA + sin2A + cos2A

Step 6The right side is a perfect square trinomial.

(sinA + cosA)2 ? sin2A + 2sinA cosA + cos2A

(sinA + cosA)2 = (sinA + cosA)2

The identity is verified.

Problem: 21 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the left side into the expression on the right.

Step 2Multiply the left side by (1 + sin y)/(1 + sin y).

Step 3Multiply the denominators on the left side.

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Step 4Use the Pythagorean identity sin2y+ cos2y= 1 or

cos2y= 1 sin2y.

Step 5Simplify.

The identity is verified.

Problem: 23 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

Step 2Use the Pythagorean identity cot2x+ 1 = csc2xor

cot2

x= csc2

x 1.

Step 3Factor the numerator.

Step 4Cancel the common factor.

cscx 1 = cscx 1

The identity is verified.

Problem: 25 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the left side into the expression on the right.

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Step 2Write tan in terms of sine and cosine. Use the identity

Step 3Cancel out the common factor.

Step 4Use the Pythagorean identity sin2+ cos2= 1.

1 = 1

The identity is verified.

Problem: 27 Set: Exercises Page: 434Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

Step 2Write the right side in terms of sine and cosine. Use the identities

Step 3Simplify the fractions.

Step 4Find a common denominator.

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Step 5Factor the numerator.

Step 6Cancel the common factor.

sinx+ cosx= sinx+ cosx

The identity is verified.

Problem: 29 Set: Exercises Page: 435Look in your textbook for this problem statement.Step 1Write the left side in terms of sine and cosine. Use the identities

Step 2

Simplify.

Step 3Solve for cosx.

Problem: 31 Set: Exercises Page: 435Look in your textbook for this problem statement.Step 1Write the left side in terms of sine and cosine. Use the identities

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Step 2Simplify.

Step 3Solve for cosx.

cosx= 0

Problem: 33 Set: Exercises Page: 435Look in your textbook for this problem statement.Step 1Use the Pythagorean identity sin2x+ cos2x= 1.

cos2

x+ 2 sinx 2 = 0

cos2x+ 2 sinx 1 1 = 0

cos2x+ 2 sinx (sin2x+ cos2x) 1 = 0

Step 2Simplify.

2 sinx sin2x 1 = 0

Step 3Multiply the left side by 1 and rearrange terms to get a perfect square trinomial.

2 sinx+ sin2x+ 1 = 0

sin2x 2 sinx+ 1 = 0

Step 4Factor the trinomial.

(sinx 1)2 = 0

Step 5Take the square root on each side.

sinx 1 = 0

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sinx= 1

Problem: 33 Set: Exercises Page: 435Look in your textbook for this problem statement.Step 1Use the Pythagorean identity sin2x+ cos2x= 1.

cos2x+ 2 sinx 2 = 0

cos2x+ 2 sinx 1 1 = 0

cos2x+ 2 sinx (sin2x+ cos2x) 1 = 0

Step 2Simplify.

2 sinx sin2x 1 = 0

Step 3Multiply the left side by 1 and rearrange terms to get a perfect square trinomial.

2 sinx+ sin2x+ 1 = 0

sin2x 2 sinx+ 1 = 0

Step 4Factor the trinomial.

(sinx 1)2 = 0

Step 5Take the square root on each side.

sinx 1 = 0

sinx= 1

Problem: 35 Set: Exercises Page: 435Look in your textbook for this problem statement.Step 1

Write the numerator as the difference of two cubes.

Use the formula for the difference of two cubes.

Step 2Simplify.

Step 3Use the Pythagorean identity sec2= 1 + tan2or

tan2 sec2= 1.

Step 4

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Use the reciprocal identity tan = 1/(cot ).