How do you prove # (sin+cos)(tan+cot)=sec+csc#?

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Answer 1 · 2015-10-17T03:22:33

See explanation.

Prove: #(sinx+cosx)(tanx+cotx)=secx+cscx#

The change I made in each step is colored red.

#[1]color(white)(XX)(sinx+cosx)(tanx+cotx)#

#[2]color(white)(XX)=(sinx+cosx)(color(red)(sinx/cosx)+color(red)(cosx/sinx))#

#[3]color(white)(XX)=color(red)(sin^2x/cosx+cosx+cos^2x/sinx+sinx)#

#[4]color(white)(XX)=(sin^2x+color(red)(cos^2x))/cosx+(cos^2x+color(red)(sin^2x))/sinx#

#[5]color(white)(XX)=(color(red)(1))/cosx+(color(red)(1))/sinx#

#[6]color(white)(XX)=color(red)(secx)+color(red)(cscx)#