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

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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

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