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Simplify without the use of calculator

[tex]\frac{\cos(-225)\sin(135)+\sin330}{\tan225}[/tex]
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Sagot :

ⲊⲧɑⲅⲊⲏɑᴅⲟᏇ

Answer:

  • -1

Solution:

[tex] \implies\quad \sf { \dfrac{cos(-225).sin(135)+sin330}{tan225}}[/tex]

[tex] \implies\quad \sf {\dfrac{cos(225)-sin(180-45)+sin(360-30)}{tan(180+45)} }[/tex]

[tex] \implies\quad \sf {\dfrac{cos(180+45).sin45-sin30}{tan45} }[/tex]

[tex] \implies\quad \sf { \dfrac{-cos45.sin45-sin30}{tan45}}[/tex]

[tex] \implies\quad \sf { \dfrac{-\dfrac{\sqrt{2}}{2}\times \dfrac{\sqrt{2}}{2}-\dfrac{1}{2}}{1}}[/tex]

[tex] \implies\quad \sf {\dfrac{-\dfrac{2}{4}-\dfrac{1}{2}}{1} }[/tex]

[tex] \implies\quad \sf {\dfrac{-2-2}{4} }[/tex]

[tex] \implies\quad \sf { -\cancel{\dfrac{4}{4}}}[/tex]

[tex] \implies\quad\underline{\underline{\pmb{ \sf {-1 }}}}[/tex]

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