How do you verify the identity #sintcsc(pi/2-t)=tant#?

Question

4585 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-17T19:05:19

see below

Left Hand Side:

#sin t csc( pi/2 -t)=sint *1/(sin(pi/2 - t))#

Use the formula #sin(A-B)=sinAcosB-cosAsinB#

#=sin t * 1/(sin (pi/2) cos t-cos (pi/2) sin t)#

#=sin t* 1/(1*cost-0*sint#

#=sint * 1/cos t#

#= sint / cos t#

#=tan t#

#:.=# Right Hand Side