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Question
Prove that tan 20° tan 35° tan 45° tan 55° tan 70° = 1
Solution
We are asked to find the value of tan 20° tan 35° tan 45° tan 55° tan 70°
`= tan(90^@ - 70^@) tan(90^@ - 55^@) tan 45^@ tan 55^@ tan 70^@`
`= cot 70^@ cot 55^@ tan 45^@ tan 55^@ tan 70^@`
`= (tan 70^@ cot 70^@)(tan 55^@ cot 55^@) tan 45`
= 1 x 1 x 1
= 1
Proved
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