Homework Soursetanx1cosxcscx1secxSolutionstarting with right side csc1sec 1
tanx/1-cosx=cscx(1+secx)
Solution
starting with right side
csc(1+sec)
=(1/sin)(1+(1/cos))
expand
=(1/sin)+(1/sincos)
=(cos+1)/(sincos)
multiply top and bottom by (cos-1)
=(cos+1)(cos-1)/(sincos)(cos-1)
=(cos^2-1)/(sincos)(cos-1)
=[(cos^2-1)/sincos]*(1/(cos-1))
=(-sin^2)/sincos/(cos-1)
=(-sin/cos)/(cos-1)
=-tan/(cos-1)
=tan/(1-cos)
verified:
right side=left side
