5.7 Proving Trigonometric Identities

5.7 Proving Trigonometric Identities

Example:
Prove each of the following trigonometric identities.
(a) cot2 x – cot2 x cos2 x = cos2 x
(b)  secx secxcosx =cose c 2 x

Solution:
(a)
cot 2 x cot 2 x cos 2 x= cos 2 x LHS:  cot 2 x cot 2 x cos 2 x = cot 2 x( 1 cos 2 x ) = cot 2 x( si n 2 x ) = cos 2 x si n 2 x ( si n 2 x ) = cos 2 x (RHS)

(b)
secx secxcosx =cose c 2 x LHS:  secx secxcosx = 1 cosx 1 cosx cosx = 1 cosx 1 cosx cos 2 x cosx = 1 cosx 1 cos 2 x cosx = 1 cosx × cosx 1 cos 2 x = 1 1 cos 2 x = 1 si n 2 x =cose c 2 x (RHS)