Question #e94cc

1 Answer
Jan 7, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)tanx=sinx/cosx#

#•color(white)(x)sin^2x+cos^2x=1#

#"consider the left hand side"#

#sinxtanx+cosx#

#=sinx xxsinx/cosx+cosx#

#=(sin^2x)/cosx+cos^2x/cosx#

#=(sin^2x+cos^2x)/cosx#

#=1/cosx=" right hand side "rArr" proven"#

#"consider the left side of the second one"#

#rArrcos^2x/sinx#

#=(1-sin^2x)/sinx#

#=1/sinx-sin^2x/sinx#

#=1/sinx-sinx=" right side "rArr"proven"#