Question

Solve (2sinxcotx+sinx+4cotx-2)/(2cotx+1)=sinx-2

Trigonometric equation and identitie
ANSWERED
asked 2021-01-05

Solve \((2\sin x\cot x+\sin x+4\cot x-2)/(2\cot x+1)=\sin x-2\)

Answers (1)

2021-01-06

Step 1 \((2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2)/(2\cot(x)+1)= Factor\ 2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2: (-2+\sin(x))(2\cot(x)+1) =((-2+\sin(x))(2\cot(x)+1))/(2\cot(x)+1)=2+\sin(x)\) Hence, given equation is true.

Step 2

Factors of \(2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2 is =2\cot(x)\sin(x)-2 \cdot 2\cot(x)-2 =2\cot(x)(\sin(x)-2)+\sin(x)-2 =2(-2+\sin(x))\cot(x)+1\cdot (-2+\sin(x)) =(-2+\sin(x))(2\cot(x)+1) (2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2)/(2\cot(x)+1)=-2+\sin(x)\)

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