Please how I can prove that ? Cos^2(t)=1/1+tan^2(t) Thanks
2 Answers
I think you mean "prove" not "improve". See below
Explanation:
Consider the RHS
So,
So RHS is now:
Now :
RHS is
QED.
Explanation:
#"to prove this is an identity either manipulate the left side"#
#"into the form of the right side or manipulate the right side"#
#"into the form of the left side"#
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)tanx=sinx/cosx" and "sin^2x+cos^2x=1#
#"consider the right side"#
#rArr1/(1+sin^2t/cos^2t)#
#=1/((cos^2t+sin^2t)/cos^2t)#
#=1/(1/cos^2t)#
#=1xxcos^2t/1=cos^2t=" left side hence proved"#