Question

Simplify without the use of calculator

Answer 1

Answer:

• -1

Solution:

$\implies\quad \sf { \dfrac{cos(-225).sin(135)+sin330}{tan225}}$

$\implies\quad \sf {\dfrac{cos(225)-sin(180-45)+sin(360-30)}{tan(180+45)} }$

$\implies\quad \sf {\dfrac{cos(180+45).sin45-sin30}{tan45} }$

$\implies\quad \sf { \dfrac{-cos45.sin45-sin30}{tan45}}$

$\implies\quad \sf { \dfrac{-\dfrac{\sqrt{2}}{2}\times \dfrac{\sqrt{2}}{2}-\dfrac{1}{2}}{1}}$

$\implies\quad \sf {\dfrac{-\dfrac{2}{4}-\dfrac{1}{2}}{1} }$

$\implies\quad \sf {\dfrac{-2-2}{4} }$

$\implies\quad \sf { -\cancel{\dfrac{4}{4}}}$

$\implies\quad\underline{\underline{\pmb{ \sf {-1 }}}}$