Question 1

Solve trigonometric function

2csc∅- 2cos^2 ∅ ×csc∅

Question 2

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

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

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

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

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

$\\ \rm\Rrightarrow (2sin^2A)/(sinA)$

$\\ \rm\Rrightarrow sinA$

Question 3

Answer:

$2\sin(\theta)$

Explanation:

$\csc(\theta)=(1)/(\sin(\theta))$

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

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

$=(2)/(\sin(\theta))-( 2cos^2(\theta))/(\sin(\theta))$

$=( 2[1-cos^2(\theta)])/(\sin(\theta))$

$=( 2sin^2(\theta))/(\sin(\theta))$

$=2\sin(\theta)$

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