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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]

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