Answered

Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Find in-depth and accurate answers to all your questions from our knowledgeable and dedicated community members.

Prove this identity. Tan^2(0)/1 + tan^2(0) = sin^2(0). Note i placed a bracket around the zeros because i didnt want to look like it is to the power of 20. And the zero is supposed to be the symbol theta.

Sagot :

Naǫidn
Use the trigonometric identities:
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta} \\ \sin^2 \theta+ \cos^2 \theta=1[/tex]

Proof:
[tex]\frac{\tan^2 \theta}{1+ \tan^2 \theta}}=\sin^2 \theta \ \ \ |\times (1+\tan^2 \theta) \\ \\ \tan^2 \theta = \sin^2 \theta (1+ \tan^2 \theta) \ \ \ |\hbox{convert } \tan \theta \hbox{ to } \frac{\sin \theta}{\cos \theta} \\ \\ (\frac{\sin \theta}{\cos \theta})^2=\sin^2 \theta (1+ (\frac{\sin \theta}{\cos \theta})^2) \\ \\ \frac{\sin^2 \theta}{\cos^2 \theta}=\sin^2 \theta(1+\frac{\sin^2 \theta}{\cos^2 \theta}) \ \ \ |\div \sin \theta[/tex]

[tex]\frac{1}{\cos^2 \theta}=1+\frac{sin^2 \theta}{\cos^2 \theta} \ \ \ |\times \cos^2 \theta \\ \\ 1=\cos^2 \theta+\sin^2 \theta \ \ \ |\hbox{convert } \cos^2 \theta+ \sin^2 \theta \hbox{ to } 1 \\ \\ 1=1[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.