Question

Simplify without the use of calculator


`(\cos(-225)\sin(135)+\sin330)/(\tan225)`
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Answer 1

• -1

Solution:

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

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

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

`\implies\quad \sf { (-cos45.sin45-sin30)/(tan45)}`

`\implies\quad \sf { (-(√(2))/(2)* (√(2))/(2)-(1)/(2))/(1)}`

`\implies\quad \sf {(-(2)/(4)-(1)/(2))/(1) }`

`\implies\quad \sf {(-2-2)/(4) }`

`\implies\quad \sf { -\cancel{(4)/(4)}}`

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