Question

sin(3 pi)/(4)+cos(7 pi)/(4) is equal to____​

Answer 1

sin 135 ° + cos 315 °

1/root 2 +1/root 2

2/root 2

Ans : root 2

Answer 2

$\huge \underline{ \underline{ \bf \purple{Solution :}}}$

$\longrightarrow \: \sf \sin \frac{3\pi}{4} + \cos \frac{7\pi}{4} \\ \\ \longrightarrow \: \sf \sin135 + \cos315 \\ \\ \longrightarrow \: \sf \sin(180 - 45) + \cos(360 - 45) \\ \\ \longrightarrow \: \sf \sin45 + \cos45 \\ \\ \longrightarrow \: \sf \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } \\ \\ \longrightarrow \: \sf \frac{1 + 1}{ \sqrt{2} } \\ \\ \longrightarrow \: \sf \frac{2}{ \sqrt{2} } \\ \\\longrightarrow \: \sf \frac{2}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ \\\longrightarrow \: \sf \frac{2 \sqrt{2} }{2} \\ \\ \longrightarrow \: \sf \sqrt{2}$