Question #75a89
2 Answers
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)1+tan^2x=sec^2x#
#•color(white)(x)tanx=sinx/cosx#
#•color(white)(x)secx=1/cosx#
#"consider the LHS"#
#rArr(tanx)/(1+tan^2x)#
#=(sinx/cosx)/(sec^2x)#
#=(sinx/cosx)/(1/cos^2x)#
#=sinx/cancel(cosx) xxcancel(cos^2x)^(cosx)#
#=sinxcosx="RHS"rArr"proven"#
See below.
Explanation:
We're trying to prove
Let's manipulate the left side since it's more complicated.
There is a trigonometric identity that states
Thus,
#tan x / (1+tan^2 x) #
#= tan x / (sec^2 x)#
#= (sin x / cos x)/(1/cos^2x) #
#=sin x / cancel(cos x) * cancel(cos^2 x)^cos x /1#
#=sin x cos x#