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Sum and difference identities
- Lesson: 1a5:48
- Lesson: 1b6:49
- Lesson: 2a12:26
- Lesson: 2b6:56
- Lesson: 3a7:42
- Lesson: 3b10:51
- Lesson: 3c10:48
- Lesson: 417:16
Sum and difference identities
Trig identities are formulas developed based on Pythagorean Theorem. These identities show us how and where to find the sine, cosine, and tangent of the sum and difference of two given angles.
Basic Concepts: Use sine ratio to calculate angles and sides (Sin = ho ), Use cosine ratio to calculate angles and sides (Cos = ha ), Use tangent ratio to calculate angles and sides (Tan = ao ), Trigonometric ratios of angles in radians
Related Concepts: Solving trigonometric equations using sum and difference identities
Lessons
Download the Trigonometry identities chart here
Formulas:
sin(A+B)
sin(A−B)
cos(A+B)
cos(A−B)
tan(A+B)
tan(A−B)
Formulas:
sin(A+B)
sin(A−B)
cos(A+B)
cos(A−B)
tan(A+B)
tan(A−B)
- 1.Simplify expressionsa)sin 24°cos 36° + cos 24°sin 36°b)1+tan52π⋅tan203πtan52π−tan203π
- 2.Prove Identitiesa)sinBsin(A−B)+cosBcos(A−B)=sinBcosBsinAb)tan(A+4π)1+tanA=1−tanA
- 3.Without using a calculator, evaluate:a)sin 15°b)sec (-105°)c)tan 1219π
- 4.Given sinA=−54 and cosB=1312,
where π≤A≤23π and 23π≤B≤2π,
find the exact value of cos(A+B)