Question

Hey guys this is chaitya from 9 th class I have a doubt in trigonometrical ratios plz help me out

prove that tan(225).cot(405)+tan(765).cot(675)=0

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Answer 1

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Answer 2

Answer:

$$\begin{lgathered}tan225^ocot405^o+cot675^otan765^o=0\\\\L=tan(180^o+45^o)cot(2\times180^o+45^o)+\dots\\\dots+cot(4\times180-45^o)tan(4\times180^o+45^o)\\\\=tan45^ocot45^o+cot(-45^o)tan45^o=1-cot45^otan45^o\\\\=1-1=0\\\\===================================\\\\tan\alpha\times cot\alpha=1\\\\cot(-\alpha)=-cot\alpha\end{lgathered}$$

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