Question #c11fc

3 Answers
Dec 19, 2017

Image reference..

Explanation:

my notebook....

Dec 19, 2017

#"see explanation"#

Explanation:

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

#•color(white)(x)sin^2x+cos^2x=1#

#•color(white)(x)tan^2x=sec^2x-1#

#"consider the left hand side"#

#(1-cos^2x)/(sec^2x-1)#

#=sin^2x/tan^2x#

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

#=cancel(sin^2x)xxcos^2x/cancel(sin^2x)#

#=cos^2x=" right hand side "rArr"verified"#

Dec 19, 2017

#"see explanation"#

Explanation:

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

#•color(white)(x)sin^2x+cos^2x=1#

#•color(white)(x)sec^2x=1/cos^2x#

#"consider the left hand side"#

#(1-cos^2x)/(sec^2x-1)#

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

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

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

#=cancel(sin^2x)xxcos^2x/cancel(sin^2x)#

#=cos^2x=" right hand side "rArr"verified"#