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Question
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Solution
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Consider `tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ`
⇒ `tan(90^circ - 80^circ) - tan(90^circ - 70^circ) tan30^circ tan70^circ tan80^circ`
⇒ `cot80^circ . cot70^circ .tan30^circ tan70^circ tan80^circ`
⇒ `tan30^circ = 1/sqrt(3)` [As tanθ cotθ = 1]
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