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Prove the identity. sin (x-y) = tanx-tany cosx cosy Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button to the right of the Rule. Statement sin(x - y) COSX COSy Validate Rule Select Rule ロ・ロ cos cot в X olo sin sec 0 9. tan Ś csc $

Prove the identity. sin (x-y) = tanx-tany cosx cosy Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button to the right of the Rule. Statement sin(x - y) COSX COSy Validate Rule Select Rule ロ・ロ cos cot в X olo sin sec 0 9. tan Ś csc $

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section: Chapter Questions
Problem 6RE
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Prove the identity. sin (x-y) cosx cosy Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button to the right of the Rule. Statement = tanx-tany sin (x - y) COS. COSy 0 Validate Rule Select Rule ロ・ロ cos cot J X 00 sin ☐sec tan csc 0/6
Transcribed Image Text:Prove the identity. sin (x-y) cosx cosy Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button to the right of the Rule. Statement = tanx-tany sin (x - y) COS. COSy 0 Validate Rule Select Rule ロ・ロ cos cot J X 00 sin ☐sec tan csc 0/6
Prove the identity. cos (x-y) sinx-sin (x-y) cosx = siny OO EXPLANATION We'll start with the left side. We'll transform it step by step until it is identical to the right side. cos (x−y) sinx-sin(x−y) cosx =(cosx cosy+ sinx siny) sinx −(sinx cosy− cosx siny) cosx =sinx cosx cosy+sin’x siny − sinx cosx cosy+cos‘x siny sin²x siny+ cos²x siny = siny (sin²x + cos²x) = siny Here is one possible answer. EANSWER = = Statement More sin²x siny + cos²x siny Sum and difference identities: cos (u-v) = cos u cos v + sinu sinv sin (u-v) = sinu cos v- cosu sin v siny (sin²x + cos²x) Algebra cos (x - y) sinx - sin(x - y) cosx = siny Algebra Algebra (cosx cosy + sinx siny) sinx − (sinx cosy – cosx siny) cosx Pythagorean identity: sin²u+ cos²u = 1 sinx cosx cosy + sin’x siny - sinx cosx cosy + cos’x siny Rule Sum and Difference Algebra Algebra Algebra Pythagorean
Transcribed Image Text:Prove the identity. cos (x-y) sinx-sin (x-y) cosx = siny OO EXPLANATION We'll start with the left side. We'll transform it step by step until it is identical to the right side. cos (x−y) sinx-sin(x−y) cosx =(cosx cosy+ sinx siny) sinx −(sinx cosy− cosx siny) cosx =sinx cosx cosy+sin’x siny − sinx cosx cosy+cos‘x siny sin²x siny+ cos²x siny = siny (sin²x + cos²x) = siny Here is one possible answer. EANSWER = = Statement More sin²x siny + cos²x siny Sum and difference identities: cos (u-v) = cos u cos v + sinu sinv sin (u-v) = sinu cos v- cosu sin v siny (sin²x + cos²x) Algebra cos (x - y) sinx - sin(x - y) cosx = siny Algebra Algebra (cosx cosy + sinx siny) sinx − (sinx cosy – cosx siny) cosx Pythagorean identity: sin²u+ cos²u = 1 sinx cosx cosy + sin’x siny - sinx cosx cosy + cos’x siny Rule Sum and Difference Algebra Algebra Algebra Pythagorean
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