Question

Solve trigonometric function 2csc∅- 2cos^2 ∅ ×csc∅

Answer 1

• Theta turned to A

$\\ \rm\Rrightarrow 2cscA-2cos^2A(cscA)$

$\\ \rm\Rrightarrow 2(1/sinA)-2cos^2A(1/sinA)$

$\\ \rm\Rrightarrow \dfrac{2}{sinA}-\dfrac{2cos^2A}{sinA}$

$\\ \rm\Rrightarrow \dfrac{2-2cos^2A}{sinA}$

$\\ \rm\Rrightarrow \dfrac{2(1-cos^2A)}{sinA}$

$\\ \rm\Rrightarrow \dfrac{2sin^2A}{sinA}$

$\\ \rm\Rrightarrow sinA$

Answer 2

Answer:

$2\sin(\theta)$

Step-by-step explanation:

$\csc(\theta)=\dfrac{1}{\sin(\theta)}$

$\sin^2(\theta)+\cos^2(\theta)=1\implies \sin^2(\theta)=1-\cos^2(\theta)$

$2\csc(\theta)- 2cos^2(\theta)\times csc(\theta)$

$=\dfrac{2}{\sin(\theta)}-\dfrac{ 2cos^2(\theta)}{\sin(\theta)}$

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

$=\dfrac{ 2sin^2(\theta)}{\sin(\theta)}$

$=2\sin(\theta)$