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Show that tan48^(@) tan 23^(@) tan 42^(@...

Show that `tan48^(@) tan 23^(@) tan 42^(@) tan 67^(@) =1`.

Text Solution

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LHS = `tan 48^(@) tan 23(@) tan42^(@) tan 67^(@)`
`" " = Cot (90^(@)- 48^(@)) cot (90^(@)- 23^(@)) tan 42^(@) tan 67^(@)`
`" " = Cot 42^(@) cos 67^(@) tan 42^(@) tan 67^(@)`
`" " =1 `
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