How do you verify the identify #costhetacottheta+sintheta=csctheta#?

2 Answers
Mar 26, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)cottheta=costheta/sintheta" and "csctheta=1/sintheta#

#•color(white)(x)sin^2theta+cos^2theta=1#

#"consider the left side"#

#costhetaxxcostheta/sintheta+sintheta#

#=cos^2theta/sintheta+sin^2theta/sintheta#

#=(cos^2theta+sin^2theta)/sintheta#

#=1/sintheta=csctheta=" right side "rArr"verified"#

Mar 26, 2018

see below

Explanation:

L.H.S: #costhetaxxcot theta +sin theta#
=#cos theta xx(frac{cos theta}sin theta) +sin theta#
=#cos^2theta//sin theta +sin theta#
=#frac{cos^2 theta +sin^2 theta}sin theta#
=#1//sin theta#
=#"cosec "theta# which is the R.H.S