Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

how do you do...
cos2x-sin2x=1-2sin2x

Sagot :

kate200468
[tex]sin (2 \alpha) =2\cdot sin \alpha \cdot cos \alpha \\cos(2 \alpha )=1-2sin^2 \alpha \\-------------------- \\cos2x-sin2x=1-2sin2x\\cos2x+sin2x=1\\1-2sin^2x+2sinx\cdot cosx=1\\-2sinx(sin x-cosx)=0\\ -2sinx=0\ \ \ \ or\ \ \ \ sinx-cosx=0\\\\1)\ -2sinx=0\ \ \Leftrightarrow\ \ sinx=0\ \ \Leftrightarrow\ \ x_1=k \pi \ \ and\ \ k\in I\\2)\ \ sinx-cosx=0\ \ \Leftrightarrow\ \ sinx=cosx\ /:cosx\ \ \ \ \ \wedge\ \ \ \ cos x \neq 0\\tanx=1\ \ \Leftrightarrow\ \ x_2= \frac{ \pi }{4} +k \pi \ \ and\ \ k\in I[/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.