Question

sin[x-π/6]+ cos[x-π/3]​

Answer 1

Answer:

See The Pic ✌️✌️❤️❣️☺️........

Answer 2

Answer:

$It \: is \: given \: that \: the \: LHS \: is \\ </p><p>sin(x + \frac{\pi}{6})−cos(x+ \frac{\pi}{3}) \\ Applying,  \\ sin(A+B)=sin \: A \: cos \: B+cos A \: sin \: B and \\ cos(A+B)=cos \: A \: cos \: B−sin \: A \: sin \: B \\ ⇒sin \: x \: cos(\frac{\pi}{6} )+cos \: x \: sin( \frac{\pi}{6})\\ −(cos \: x \: cos ( \frac{\pi}{3})−sin \: x \: sin( \frac{\pi}{3})) \\ ⇒sin \: x( \frac{ \sqrt{3} }{2} )+cos \: x( \frac{1}{2} )−cos \: x( \frac{1}{2} )+sin \: x( \frac{ \sqrt{3} }{ 2 }) \\=> 2×sin \: x( \frac{ \sqrt{3} }{2}) \\ ⇒√3 \: sin \: x</p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p></p><p>$