How do you verify #(sintheta-1)(tantheta+sectheta)=-costheta#?

Question

1457 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-14T19:43:12

see below

#(sintheta-1)(tantheta+sectheta)=-costheta#

Left Side : #=(sintheta-1)(tantheta+sectheta)#

#=(sintheta-1)(sintheta/costheta+1/costheta)#

#=(sintheta-1)((sintheta+1)/costheta)#

#=(sin^2theta-1)/costheta#

#=(-(1-sin^2theta))/costheta#

#=(-cos^2theta)/costheta#

#=(-cos^cancel2theta)/cancelcostheta#

#=-cos theta#

#:.=# Right Side