Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

solve trigonometric function

2csc∅- 2cos^2 ∅ ×csc∅

Sagot :

semsee45

Answer:

[tex]2\sin(\theta)[/tex]

Step-by-step explanation:

[tex]\csc(\theta)=\dfrac{1}{\sin(\theta)}[/tex]

[tex]\sin^2(\theta)+\cos^2(\theta)=1\implies \sin^2(\theta)=1-\cos^2(\theta)[/tex]

[tex]2\csc(\theta)- 2cos^2(\theta)\times csc(\theta)[/tex]

[tex]=\dfrac{2}{\sin(\theta)}-\dfrac{ 2cos^2(\theta)}{\sin(\theta)}[/tex]

[tex]=\dfrac{ 2[1-cos^2(\theta)]}{\sin(\theta)}[/tex]

[tex]=\dfrac{ 2sin^2(\theta)}{\sin(\theta)}[/tex]

[tex]=2\sin(\theta)[/tex]
  • Theta turned to A

[tex]\\ \rm\Rrightarrow 2cscA-2cos^2A(cscA)[/tex]

[tex]\\ \rm\Rrightarrow 2(1/sinA)-2cos^2A(1/sinA)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2}{sinA}-\dfrac{2cos^2A}{sinA}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2-2cos^2A}{sinA}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2(1-cos^2A)}{sinA}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2sin^2A}{sinA}[/tex]

[tex]\\ \rm\Rrightarrow sinA[/tex]

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.