Question

if sinx+cosx=0and x lies in fourth quadrant then find sinx and cosx​

Answer 1

$\bold {\huge {\mathfrak {\underline{Hello!}}}}$

$\star \: \: \underline \blue{Solution} \: \: \star$

$(sin x + cosx) = 0$

$\longrightarrow {(sin \: x + cos \: x)}^{2} = 0$

$\longrightarrow {sin}^{2} x + {cos}^{2} x + 2 \: sinx \: cosx = 0$

$\longrightarrow1 + 2 \: sinx \: cosx = 0$

$\longrightarrow \: sin2x = - 1$

$\longrightarrow \: sin 2x = sin\frac{3\pi}{2}$

$\longrightarrow \: 2x = \frac{3\pi}{2}$

$\longrightarrow \: x = \frac{3\pi}{4}$

Hance,

$\boxed {\mathtt{sin \frac{3 \pi}{4} = \frac{1}{ \sqrt{2} } }}$

$\boxed{ \mathtt{cos \: \frac{3\pi}{4} = - \frac{1}{ \sqrt{2} } }}$