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Prove that tan 56^(@) =("cos " 11^(@)...

Prove that `tan 56^(@) =("cos " 11^(@) + "sin " 11^(@))/("cos " 11^(@) - "sin "11^(@))`

Text Solution

Verified by Experts

We have
LHS = tan `56^(@) = " tan " (45^(@)+11^(@))`
`=("tan " 45^(@) + " tan " 11^(@))/(1- " tan " 45^(@) "tan " 11^(@))`
`=(1+"tan " 11^(@))/(1-"tan " 11^(@))`
`=(1+("sin "11^(@))/("cos "11^(@)))/(1-("sin " 11^(@))/("cos " 11^(@)))= ("cos "11^(@) + "sin " 11^(@))/("cos "11^(@) -"sin " 11^(@)) =RHS`
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