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B The following identities involve the reciprocal, quotient, and Pythagorean relationships. Prove each one. 1. sin x tan x = sec.x- cos x

B The following identities involve the reciprocal, quotient, and Pythagorean relationships. Prove each one. 1. sin x tan x = sec.x- cos x

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 43E
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8 1. 2. 3. 4. 5. 6. The following identities involve the reciprocal, quotient, and Pythagorean relationships. Prove each one. sin x tan x = sec.x <- COS X cos¹.r cos¹ tan x 7. (sec x - cos x)(csc x - sin x) = 1 + tan² x 8. cos x + sin x = 1 - 3 sin²x + 3 sinº x 23. The following involve the addition and subtraction formulas. sin(x + y) 10. 1 cot x tan y sin x cos y 11. cos(x + y)cos y + sin(x + y)sin y = cos x sin(x - y) 12. sin x - tan y cos x = cos y 13. cos(3 + x) + sin(²-x) = 26. x - sin¹ x = 1 - 2 sin².r csc² x + secr=csc²x secr cos²x cos² y + sin² x sin² y + sin³x cos² y + sin' y cos x = 1 sec² x - sec² y = tan² x - tan² y 15. sin(x + y)sin(x - y) = cosy - cos²x sin² x - sin³ cos' x - sin² y tan x + tan y cot x + cot y 16. tan(x + y)tan(x - y) = = (tan x)(tan y) 30. 19. sin(-x)cot(+ x) = − sin x 20. cos(-x) + cos(-x) = cos(# + x) + cos x 31. CSC(-x) cos(-x) sec(# + x) cos(+ x) 32. The following involve related and co-related angles. 28. 2 csc 2x = sec .x csc X 29. 2 cot 2x = cot * -tan cos 2r 1 + sin 2x cos x - sin x cos x + sin x 1 - cos 2r + sin 2x 1 + cos 2r + sin 2r = cot² x The following involve the double angle formulas. sin 2x 1 + cos 2r cas y = tan x =sec 2x - tan 2r = tan x
Transcribed Image Text:8 1. 2. 3. 4. 5. 6. The following identities involve the reciprocal, quotient, and Pythagorean relationships. Prove each one. sin x tan x = sec.x <- COS X cos¹.r cos¹ tan x 7. (sec x - cos x)(csc x - sin x) = 1 + tan² x 8. cos x + sin x = 1 - 3 sin²x + 3 sinº x 23. The following involve the addition and subtraction formulas. sin(x + y) 10. 1 cot x tan y sin x cos y 11. cos(x + y)cos y + sin(x + y)sin y = cos x sin(x - y) 12. sin x - tan y cos x = cos y 13. cos(3 + x) + sin(²-x) = 26. x - sin¹ x = 1 - 2 sin².r csc² x + secr=csc²x secr cos²x cos² y + sin² x sin² y + sin³x cos² y + sin' y cos x = 1 sec² x - sec² y = tan² x - tan² y 15. sin(x + y)sin(x - y) = cosy - cos²x sin² x - sin³ cos' x - sin² y tan x + tan y cot x + cot y 16. tan(x + y)tan(x - y) = = (tan x)(tan y) 30. 19. sin(-x)cot(+ x) = − sin x 20. cos(-x) + cos(-x) = cos(# + x) + cos x 31. CSC(-x) cos(-x) sec(# + x) cos(+ x) 32. The following involve related and co-related angles. 28. 2 csc 2x = sec .x csc X 29. 2 cot 2x = cot * -tan cos 2r 1 + sin 2x cos x - sin x cos x + sin x 1 - cos 2r + sin 2x 1 + cos 2r + sin 2r = cot² x The following involve the double angle formulas. sin 2x 1 + cos 2r cas y = tan x =sec 2x - tan 2r = tan x
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