Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Prove that tan 225 cot 405 + cot 675 tan 765 = 0

Sagot :

[tex]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[/tex]
kate200468
[tex]tan 225^0 cot 405^0 + cot 675^0 tan 765^0=\\=tan(180^0+45^0)\cdot cot(2\cdot180^0+45^0)+\\+cot(4\cdot180^0-45^0)\cdot tan(4\cdot180^0+45^0)=\\=tan45^0\cdot cot45^0-cot45^0\cdot tan45^0=1\cdot1-1\cdot1=1-1=0[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.