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Prove that : tan 70^(@) = tan 20^(@) + 2...

Prove that : `tan 70^(@) = tan 20^(@) + 2 tan 50^(@)`

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Prove that tan 70^(@) - tan 20^(@) - 2 tan 40^(@) = 4 tan 10^(@) .

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Prove that tan 9^(@) - tan 27^(@) -tan 63^(@) + tan 81^(@) =4

Prove that: tan10^(@) tan20^(@)tan70^(@)tan80^(@)=1

tan 20^(@) tan 40^(@) tan 80^(@) = tan 60^(@)

Prove that: tan10^(@)tan50^(@)+tan50^(@)tan70^(@)+tan70^(@)tan170^(@)=3

Evaluate without using trigonometric tables : tan 20^(@) tan 40^(@) tan 50^(@) tan 70^(@)

Without using trigonometric tables , prove that : (i) tan20^(@)tan40^(@) tan45^(@)tan50^(@)tan70^(@)=1 (ii) tan1^(@) tan2^(@)tan60^(@)tan88^(@)tan89^(@)=sqrt(3) (iii) cot5^(@)cot10^(@)cot30^(@)cot80^(@)cot85^(@)=sqrt(3) (iv) 4sin10^(@)sin20^(@)sin30^(@)sec70^(@)sec80^(@)=2

Prove that: (a) tan 20^(@)tan40^(@)tan60^(@)tan 80^(@)=3 (b) tan9^(@)-tan27^(@)-tan63^(@)+tan81^(@)=4

Prove that tan 70^(@)=cot70^(@)++2cot40^(@)