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Question

Prove tan(225o)cot(405o)tan(7650)cot(675o)=0

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Solution

tan(225)cot(405)tan(765)cot(675)

=tan225(cot405)+tan765cot675

=tan(180+45)cot(360+45)+tan(360×2+45)cot(360×245)

=tan45cot45+tan45(cot45)

=tan45×1tan45tan45×1tan45

=0

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