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Prove that tan 70^(@) = "tan " 20^(@) ...

Prove that tan `70^(@) = "tan " 20^(@) + 2"tan " 50^(@)`

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`tan 70^(@)=tan(50^(@)+20^(@))`
`=(tan 50^(@)+tan 20^(@))/(1-tan 50^(@)tan 20^(@))`
or `tan 70^(@)(1-tan50^(@)tan 20^(@))=tan 50^(@)+tan 20^(@)`
or `tan 70^(@)-tan 50^(@)tan 20^(@)tan 70^(@)=tan50^(@)+tan 20^(@)`
or `tan70^(@)=tan70^(@)tan 50^(@)tan 20^(@)+tan 50^(@)+tan 20^(@)`
`=tan(90^(@)-20^(@))tan 50^(@)tan20^(@)+tan50^(@)+tan20^(@)`
`=cot20^(@)tan20^(@)+tan50^(@)+tan20^(@)`
`=tan50^(@)+tan50^(@)+tan20^(@)`
`=2 tan 50^(@)+tan 20^(@)`
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