Question 1132184
(a) 


{{{(tan(x) - cos(x))/(sin(x)cos(x) )= sec^2(x) - csc^2(x) }}}


start with


{{{(tan(x) - cos(x))/(sin(x)cos(x) )}}}


={{{tan(x)/(sin(x)cos(x) ) - cos(x)/(sin(x)cos(x) )}}}


={{{(sin(x)/cos(x))/(sin(x)cos(x) ) - cos(x)/(sin(x)cos(x) )}}}


={{{(cross(sin(x))1/cos(x))/(cross(sin(x))cos(x) ) - cross(cos(x))1/(sin(x)cross(cos(x)) )}}}


={{{(1/cos(x))/cos(x)  - 1/sin(x)}}}


={{{1/cos^2(x)  - 1/sin(x)}}}


={{{sec^2(x) - csc(x)}}}=>this is your solution, it’s not {{{csc^2(x) }}}(you probably made mistake while typing)



(b) 


{{{sin^4(x) + cos^4(x) = 1- 2sin^2(x)cos^2(x )}}}


start with


{{{sin^4(x) + cos^4(x)}}}


={{{sin^2(x) sin^2(x) + cos^2(x)cos^2(x)}}}


={{{(1-cos^2(x) )sin^2(x) + (1-sin^2(x))cos^2(x)}}}


={{{sin^2(x)-cos^2(x) *sin^2(x) + cos^2(x)-sin^2(x)*cos^2(x)}}}


={{{sin^2(x)+ cos^2(x)-2sin^2(x)*cos^2(x)}}}


={{{1-2sin^2(x)*cos^2(x)}}}