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TRIG.87 Verify an identity by transforming one side only Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.87 Verify an identity by transforming one side only. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.87 Verify an identity by transforming one side only - Verify an identity by transforming one side only

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Trigonometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related TRIG.87 Verify an identity by transforming one side only skill assessments:

Problem 1Difficulty: Mastery

Work from the left side only to verify the identity: (sin 3x − sin x) ÷ (cos x − cos 3x) = cot 2x Which option shows a correct equivalent rewrite of the LEFT side?

Asin 3x − sin x = 2 cos 2x sin x

Bsin 3x − sin x = −2 cos 2x sin x

Csin 3x − sin x = 2 sin 2x sin x

Dsin 3x − sin x = 2 sin 2x cos x

Solution & Explanation:Use sin A − sin B = 2 cos((A+B)/2) sin((A−B)/2). With A=3x and B=x you get 2 cos 2x sin x. Also cos x − cos 3x = 2 sin 2x sin x, so the ratio becomes cos 2x ÷ sin 2x = cot 2x.

Problem 2Difficulty: Mastery

Keep the expression equivalent. Which rewrite of the left side helps reach the right side? (cos 2x − cos 4x) ÷ (sin 4x + sin 2x) = tan x Which option shows a correct equivalent rewrite of the LEFT side?

Acos 2x − cos 4x = 2 cos 3x cos x

Bcos 2x − cos 4x = −2 cos 3x sin x

Ccos 2x − cos 4x = 2 sin 3x sin x

Dcos 2x − cos 4x = −2 sin 3x sin(−x)

Solution & Explanation:Use cos A − cos B = −2 sin((A+B)/2) sin((A−B)/2). With A=2x and B=4x, the half-sum is 3x and half-difference is −x, so the numerator becomes 2 sin 3x sin x. The denominator is 2 sin 3x cos x, so the ratio is tan x.

Problem 3Difficulty: Mastery

Only transform the left side. Which step is valid? (sin 3x + sin x) ÷ (cos 3x + cos x) = tan 2x Which option shows a correct equivalent rewrite of the LEFT side?

Asin 3x + sin x = 2 cos 2x sin x

Bsin 3x + sin x = 2 sin 2x cos x

Csin 3x + sin x = 2 sin x cos 2x

Dsin 3x + sin x = 2 sin 2x sin x

Solution & Explanation:Apply sin A + sin B = 2 sin((A+B)/2) cos((A−B)/2). Here it gives 2 sin 2x cos x, and cos 3x + cos x = 2 cos 2x cos x, so the ratio is tan 2x.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard TRIG.87 (Verify an identity by transforming one side only).