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Problem: 15 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Use the halfangle identity

Since 75 is in Quadrant I, choose the positive sine value.

Step 2Write 75 as a halfangle.

Step 3Substitute 3/2 for cos 150 .

Step 4Simplify.

Problem: 17 Set: Exercises Page: 454Look in your textbook for this problem statement.

Step 1Use the halfangle identity

Since 3/8 is in Quadrant I, choose the positive sine value.

Step 2Write 3/8 as a halfangle.

Step 3Substitute 2/2 for cos 3/4.

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Step 4Simplify.

Problem: 19 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Use the halfangle identity

.

Since 22.5 is in Quadrant I, choose the positive tangent value.

Step 2Write 22.5 as a halfangle.

Step 3

Step 4Rationalize the denominator.

Problem: 21 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Use the Pythagorean identity sin2+ cos2= 1.

sin2= 1 cos2. Since is in Quadrant I, sin is positive.

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Step 2Find tan .

Step 3Find sin 2.

Step 4Find cos 2. Use any of the doubleangle identities for cosine.

Step 5Find tan 2.

Problem: 23 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Use the Pythagorean identity sec2= 1 + tan2. Since is in Quadrant II, sec is negative.

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Step 2

Step 3Use the Pythagorean identity sin2+ cos2= 1.

sin2= 1 cos2. Since is in Quadrant II, sin is positive.

Step 4Find sin 2.

Step 5Find cos 2. Use any of the doubleangle identities for cosine.

Step 6Find tan 2.

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Problem: 25 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Use the Pythagorean identity csc2= 1 + cot2. Since is in Quadrant III, csc is negative.

Step 2

Step 3Use the Pythagorean identity sin2+ cos2= 1.

cos2= 1 sin2. Since is in Quadrant III, cos is negative.

Step 4Find tan .

Step 5Find sin 2.

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Step 6Find cos 2. Use any of the doubleangle identities for cosine.

Step 7Find tan 2.

Problem: 27 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Use the Pythagorean identity sin2+ cos2= 1.

sin2= 1 cos2. Since is in Quadrant II, sin is positive.

Step 2Find tan .

Step 3Find tan 2.

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Problem: 29 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

Step 2Use the identity cos 2A = cos2A sin2A.

Step 3Factor the numerator.

Step 4Simplify.

The identity is verified.

Problem: 31 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

Step 2Use the identity cos 2x= 2cos2x 1.

Step 3Factor the numerator.

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Step 4Simplify.

The identity is verified.

Problem: 33 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Transform the right side into the expression on the left.

Step 2Write A as a halfangle.

Step 3Use the identities

Step 4Simplify.

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Step 5Use the quotient identity for tangent.

The identity is verified.

Problem: 35 Set: Exercises Page: 454Look in your textbook for this problem statement.Step 1Transform the left side into the expression on the right.

Step 2Write 3xas 2x+ x.

Step 3Use the sum identity for cosine.

Step 4Use the identities

cos 2x= 2 cos2x 1 and

sin 2x= 2 sin xcos x

Step 5Simplify.

Step 6Use the Pythagorean identity sin2x+ cos2x= 1. Therefore sin2x= 1 cos2x.

Step 7Simplify.

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The identity is verified.