`sin(t)csc(pi/2 - t) = tan(t)` Verfiy the identity.

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Chapter 5, 5.2 - Problem 45 - Precalculus (3rd Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Verify the identity: `sin(t)csc(pi/2-t)=tan(t)`

Simplify the left side of the equation by using the cofunction identity

csc((pi/2)-t)=sec(t).

`sin(t)sec(t)=tan(t)`

Simplify the left side of the equation by using the reciprocal identity

sec(t)=1/cos(t).

`sin(t)*1/cos(t)=tan(t)`

`sin(t)/cos(t)=tan(t)`

`tan(t)=tan(t)`  

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