Respuestas
Respuesta:
a )
tan² - sen² = tan² . sen²
( sen² / cos² ) - sen² = tan² . sen²
( sen² - sen² . cos² ) / cos² = tan² . sen²
sen² ( 1 - cos² ) / cos² = tan² . sen²
tan² . sen² = tan² . sen² → Solución
b )
( sec - tan ) ( csc + 1 ) = cot
( ( 1 / cos ) - ( sen / cos ) ) . ( ( 1 / sen ) + 1 ) = cot
( ( 1 - sen ) / cos ) . ( ( 1 + sen ) / sen ) = cot
( 1 - sen² ) / ( sen . cos ) = cot
cos² / ( sen . cos ) = cot
cos / sen = cot
cot = cot → Solución
c )
( 1 - sen ) . ( sec + tan ) = cos
( 1 - sen ) . ( ( 1 / cos ) + ( sen / cos ) ) = cos
( 1 - sen ) . ( ( 1 + sen ) / cos ) = cos
( 1 - sen² ) / cos = cos
cos² / cos = cos
cos = cos → Solución
d )
sen / ( 1 - cos ) = cos + cot
( sen / ( 1 - cos ) ) . ( ( 1 + cos ) / ( 1 + cos ) ) = cos + cot
( ( sen . ( 1 + cos ) ) / ( ( 1 - cos ) . ( 1 + cos ) ) = cosec + cot
( sen . ( 1 + cos ) ) / ( 1 - cos² ) = cosec + cot
sen ( 1 + cos ) / sen² = cosec + cot
( 1 + cos ) / sen = cosec + cot
( 1 / sen ) + ( cos / sen ) = cosec + cot
cosec + cot = cosec + cot → Solución