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Prove that: tan(-225^0)cot(-405^0)-tan(-...

Prove that: `tan(-225^0)cot(-405^0)-tan(-765^0)cot(675^0)=0`

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Consider LHS
`tan(-225^0)cot(-405^0)-tan(-765^0)cot(675^0)` `= tan (90° × 2 + 45°) cot (90° × 4 + 45°) + tan (90° × 8 + 45°) cot (90° × 7 + 45°)`
As we know, when n is odd, cot → tan.
`= tan 45° cot 45° + tan 45° [-tan 45°] ` ...
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