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Provet that "tan "((pi)/(4)+(x)/(2)) ...

Provet that
`"tan "((pi)/(4)+(x)/(2)) = " tan x + sec x "`

Text Solution

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`RHS= ((1)/(cos x) +(sin x)/(cos x)) =((1 + sin x))/(cos x) =(1 - cos ((pi)/(2) +x))/(sin .((pi)/(2)+x))`
`=(2 sin^(2) ((pi)/(4)+(x)/(2)))/(2 sin ((pi)/(4)+(x)/(2)) cos ((pi)/(4)+(x)/(2)))=tan ((pi)/(4)+(x)/(2))= LHS`
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