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1. Trigonometric Identities and Equation, Some Standard. Formula, 1+ cos 8, 20., cot, where 0= 2n n, 1- cos e, 1. sin A+ cos A = 1, 2. 1+ tan A sec" A or, sec A-tan A 1, 21. sin 36 3 sin 8-4 sin" e, 22. cos 30 = 4 cos' 0-3 cos 0, or, sec At tan A, where A nat, sec A - tan A, 3tan 8- tane, 23. tan 30 =, ne z., 1-3tane, 3., 1+ cor A = cosee A, or,, cosec'A - cotA =1, sin 2" A, or,, 24. cos A cos 2 A cos 2 A... cos 2 'A, 2" sin A, cosec A+ cot A, where A nn. neZ, cosec A - cot A, 25. sin O sin (60°-0) sin(60" + 0)D, 1, sin 30, 4. sin (A + B) sin A cos B+ cos A sin B, 1, 5., sin (A- B) = sin A cos B - cos A sin B, 26. cos e cos (60°-0) cos(60°+ 8)= cos 30, 6. cos (A + B) = cos A cos B- sin A sin B, 27. tan e tan (60° -0) tan (60°- 6) = tan 3 8, 7. cos (A-B) cos A cos B + sin A sin B, A+B, A -B, tan At tan B, 28. sin A + sin 8 = 2 sin, 8., tan (A + B), where, 1- tan A tan B, (A BY, 2 sin, cos, (A B, 29. sin A sin B, 2., tan A- tan B, 30. cos A + cos B = 2cos, 2., A+B, A-B, cos, 9., tan (A - B) =, and, A B mn+, 1+ tan A tan B, (A+B, A-B, sin, cot A cot 8-1, cot A + cot B, cot A cot B +1, cot B - cot A, 31. cos A - cos B =- 2sin, cot (A + B) =, 10., where Ann, B nn, and, At Bnn, sin (A+ B)), cos A cos B, cot (A - B) =, 32. tan A + tan B =, where A, B nn+, 11. sin (A + 8) sin (A - B) = sin' A- sinB = cot 8 - cos' A, sin (A B)|, cos A cos B, 33. tan A, tan B =, 12. cos (A + B)cos(A- B) cos A sin B - cos B sin A, 2 tan 0, 13. sin 20 2sin Ocos 0, sin (A + B), 1+ tan 0, 34. cot A + cnt B =, where A, B na, nez, sin A sin B, 14. cos 20 = cos' 0-sin e, sin (B - A), 35. cot A- oot B =, where A, B n, neZ., cos 20 = 2 cose-1, sin A sin B, cos 20 =1-2sin0, 1- tane, 1+ tan?0, 36. 2 sin A cos B = sin (A + B) + sin (A - B), 37. 2cos A sin B = sin (A + B)- sin (A-B), 38. 2cos A cos B = cos (A + B) + cos (A - B), cos 20 =, 15. 1+ cos 26e 2cos" 6, 1- cos 20 = 2sine, 39. 2 sin A sin B = cos (A-B)-cos (A+ B), 1- cos 28, or,, 1- cos 28, = cos a, = sin 8, 40. sin (A t B C) - sin A cos B cosCi cos A sin B cosC, * cos A cos B sin C sin A sin B sinC, 2 tan 8, 16. tan 2H =, where 8= (2n + 1, 1-tan 0, or,, 1- cos e, 17., where e= 2n n, sin (A + B C), = tan, sin 0, = cos A cos B cosC (tan A + tan B+ tan C, 1+ cos 0, 18., sin e, cot, where 0 (2n + 1)n, - tan A tan B tan C), 41. cos (A + B + C) = cos A cos B cosC - sin A sin B cosC, 1- cos It, 19., 1+cos 0, = tan, where 8= (2n + 1)n, - sin A cos B sin C -cos A sin B sin C or,