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

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

Text Solution

Verified by Experts

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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What is the value of (tan 9^(@) tan 23^(@) tan 60^(@) tan67^(@) tan 81^(@))/("cosec"^(2)72^(@)+cos^(2)15^(@)-tan^(2)18^(@)+cos^(2)75^(@))? (a) (1)/(2 sqrt(3)) (b) (sqrt(3))/(2) (c) (1)/(sqrt(3)) (d) 2 sqrt(3)

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`(sqrt(3))/(2)`

`(1)/(sqrt(3))`

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The value of tan 7^(@) tan 23^(@) tan39^(@) tan 60^(@) tan 51^(@) tan 67^(@) tan 83^(@) is

`sqrt(3)`