Question

Trigonometric Help Plz?

Answer 1

1)


`\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ cos(\theta )=√(1-sin^2(\theta ))\\\\ -------------------------------\\\\ sin(x)=cos(x)-1\implies sin(x)=√(1-sin^2(x))-1`


`\bf sin(x)+1=√(1-sin^2(x))\implies [sin(x)+1]^2=1-sin^2(x) \\\\\\ sin^2(x)+2sin(x)+1=1-sin^2(x)\implies 2sin^2(x)+2sin(x)=0 \\\\\\ 2sin(x)[sin(x)+1]=0\implies \begin{cases} 2sin(x)=0\\ sin(x)=0\\ \measuredangle x=0~,~\pi ~,~2\pi \\ -------\\ sin(x)+1=0\\ sin(x)=-1\\ \measuredangle x=(3\pi )/(2) \end{cases}`



2)


`\bf 3sin(x)+cos^2(x)=2 \\\\\\ 3sin(x)+[1-sin^2(x)]=2 \\\\\\ 3sin(x)-sin^2(x)+1=2 \\\\\\ 3sin(x)-sin^2(x)-1=0 \\\\\\ sin^2(x)-3sin(x)+1=0 \\\\\\ \boxed{[sin(x)-3][sin(x)+1]=0}\impliedby \textit{check closely this }FOIL`