x = cos x – ( – cos x ) = cos x – Again, cos x = cos x – sin x = – sin x – sin x = – sin x . We have cos x = cos x – sin x = cos sin cos sin Dividing numerator and denominator by cos x , we get cos x = – tan + tan x , π π ≠ , where n is an integer . sin x = sin x cos x = 2tan + tan π π ≠ , where n is an integer We have sin ( x + y ) = sin x cos y + cos x sin y Replacing y by x , we get sin x = sin x cos x . Again sin x = 2sin cos cos sin MATHEMATICS Dividing each term by cos x , we get sin x = 2tan tan .
tan x = 2tan – tan if π π ≠ , where n is an integer We know that tan ( x + y ) = tan tan tan tan – Replacing y by x , we get tan tan tan . sin x = sin x – sin x We have, sin x = sin ( x + x ) = sin x cos x + cos x sin x = sin x cos x cos x + ( – 2sin x ) sin x = sin x ( – sin x ) + sin x – sin x = sin x – sin x + sin x – sin x = sin x – sin x . cos x = cos x – cos x We have, cos x = cos (