Question

por favor es urgente. TRIGONOMETRIA

Answer 1

1)

( sec x + tg x ).(1 - sen x ) = cos x
( 1/cos x + sen x/cos x ) . ( 1 - sen x ) = cos x
( 1 + sen x)/cos x . ( 1 - sen x ) = cos x
( 1 - sen² x ) / cos x = cos x
cos² x / cos x = cos x
cos x = cos x

2)

( tg x + cos x )/ sen x = sec x + cotg x
( sen x/cos x + cos x ) . 1/sen x = sec x + cotg x
( sen x + cos² x )/ cos x . 1 / sen x = sec x + cotg x
sen x/cos x.sen x      + cos² x / cos x.sen x = sec x + cotg x
1/cos x + cos x/sen x = sec x + cotg x
sec x + cotg x = sec x + cotg x

3)

cos² x - sen² x = 2cos² x - 1
cos² x - ( 1 - cos² x ) = 2cos² x - 1
cos² x -1 + cos² x = 2cos² x - 1
2cos² x - 1 = 2cos² x - 1

4)

cos² x ( sec² x - 1 ) = sen² x
cos² x ( 1/cos² x - 1) = sen² x
1 - cos² x = sen² x
sen² x = sen² x

5)

( tg x + cotg x ) . tg x = sec² x
( sen x/ cos x + cos x/sen x ) . sen x/cos x = sec² x
( sen² x + cos² x )/cos x. sen x    . ( sen x /cos x )= sec² x
1/cos² x = sec² x
sec² x = sec² x