How do you verify #(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x#?
2 Answers
Pretty sure the question is
Explanation:
Some basic knowledge to begin with:
1.
2.
3.
Let's start from the left hand side
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)tanx=sinx/cosx" and "cotx=cosx/sinx#
#•color(white)(x)sin^2x+cos^2x=1#
#rArrsin^2x=1-cos^2x#
#"consider the left side"#
#"distributing the parenthesis"#
#sinx xxsinx/cancel(cosx)xxcancel(cosx)-cancel(sinx)xxcosx/cancel(sinx)xxcosx#
#=sin^2x-cos^2x#
#=(1-cos^2x)-cos^2x#
#=1-2cos^2x=" right side "rArr"verified"#