IDENTITIES INVOLVING cos²x + sin²x = 1 and tan x = sin x/cos x
1.
2.
Prove that
1
1
 tan x 
tan x
sin x cos x
(a)
2 cos2A + 3 sin2A = 3  cos2A
(c)
(2 cosB + 3 sin B)2 + (3cos B  2 sin B)2 = 13
(d)
(1 + sin x)(1  sin x) = cos2x
Show that
(b)
(e)
sin .tan =
1  cos2 
cos
( 2 cos x  5 sin x ) 2  ( 5 cos x  2 sin x) 2  29