Prove that `cot12^(@)cot38^(@)cot52^(@)cot78^(@)cot60^(@)=(1)/(sqrt3)` – InterviewSolution

InterviewSolution

1.	Prove that `cot12^(@)cot38^(@)cot52^(@)cot78^(@)cot60^(@)=(1)/(sqrt3)`
Answer» `cot12^(@)cot38^(@)cot52^(@)cot78^(@)cot60^(@)` `=(cot12^(@)cot78^(@))(cot38^(@)cot52^(@))cot60^(@)` `={cot12^(@)cot(90^(@)-12^(@))}{cot38^(@)cot(90^(@)-38^(@))}cot60^(@)` `=(cot12^(@)tan12^(@))(cot38^(@)tan38^(@))cot60^(@)`. `=1xx1xx(1)/(sqrt3)=(1)/(sqrt3)` Hence `cot12^(@)cot38^(@)cot52^(@)cot78^(@)cot60^(@)=(1)/(sqrt3)`

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