How do you prove $(1+tany)/(1+coty)=secy/cscy$ ?

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Answer 1 · 2016-08-25T03:14:52

See below.

Apply the following identities:

• $tantheta = sintheta/costheta$

• $cottheta = 1/tantheta = 1/(sintheta/costheta) = costheta/sintheta$

• $sectheta = 1/costheta$

• $csctheta= 1/sintheta$

Start the simplification process on both sides.

$(1 + siny/cosy)/(1 + cosy/siny) = (1/cosy)/(1/siny)$

Put on a common denominator:

$((cosy + siny)/cosy)/((siny + cosy)/siny) = 1/cosy xx siny/1$

$(cosy + siny)/cosy xx siny/(siny + cosy) = siny/cosy$

$(cancel(cosy + siny))/cosy xx siny/(cancel(siny + cosy)) = siny/cosy$

$siny/cosy = siny/cosy$

Identity proved!!

Hopefully this helps!

How do you prove (1+tany)/(1+coty)=secy/cscy(1+tany)/(1+coty)=secy/cscy?