How do you evaluate $sin(-175) * tan(185°) * cos(355)+sin(-85°) * cos(365°)$ ?

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Answer 1 · 2017-09-12T14:49:59

$sin(-175^@)*tan(185^@)*cos(355^@)+sin(-85^@)*cos(365^@)=-1$

$sin(-175^@)*tan(185^@)*cos(355^@)+sin(-85^@)*cos(365^@)$

and as $sin(-A)=-sinA$ , this is equal to

$-sin175^@*tan(185^@)*cos(355^@)-sin85^@*cos(365^@)$

= $-sin(180^@-5^@)*tan(180^@+5^@)*cos(360^@-5^@)-sin(90^@-5^@)cos(360^@+5^@)$

= $-sin5^@*tan5^@*cos5^@-cos5^@*cos5^@$

= $-sin5^@*(sin5^@)/(cos5^@)*cos5^@-cos^2 5^@$

= $-sin^2 5^@-cos^2 5^@$

= $-(sin^2 5^@+cos^2 5^@)$

= $-1$

How do you evaluate sin(-175) * tan(185°) * cos(355)+sin(-85°) * cos(365°)sin(-175) * tan(185°) * cos(355)+sin(-85°) * cos(365°)?