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Trigonometric identities

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2 Answers

tan(u)*(csc(u) - sin(u) = tan(u)*(1/sin(u) - sin(u))
                                 = (sin(u)/cos(u))*(1/sin(u) - sin(u))
                                 = 1/cos(u) - sin^2(u)/cos(u)
                                 = (1 - sin^2(u))/cos(u)
                                 = (cos^2(u))/cos(u)
                                 = cos(u)
tan U = sin U/cos U
csc U = 1/sin U
 
(sin U/cos U)*(1/sin U - sin U)
(sin U/cos U)*((1-sin2U)sin U)    generate common denominator for expression on right, sin2/sin is same as sin
 
1-sin2 = cos2
 
(sin U/cos U)*(cos2 U/sin U)
cos2 U/cos U = cos U