Question #603e4

1 Answer
Jan 22, 2017

You need to multiply out the brackets and use #cos^2 x+sin^2 x=1# and #tan x = sin x/ cos x#

Explanation:

#(1-cos x)(1+1/(cos x))#
Multiply out the brackets:
#=1 xx 1 -1 * cosx +1xx1/(cos x) - (cos x)/(cos x )#
#=1-cos x +1/(cos x)-1#
Cancel the #1#'s:
#=-cos x + 1/(cos x)#
Put over a common denominator:
#=(-cos^2 x+1)/(cos x)#
Use Pythagoras: #cos^2 x + sin^2 x = 1#
#=sin^2x/cosx#

#=(sin x xx sin x)/cos x#
Use #tan x = sin x /cos x#
#=tan x sin x#