Without using a calculator, evaluate?

Without using a calculator, evaluate:

(Sin210 + 2cos210) / sec300

1 Answer
Jim G.
Jul 3, 2018

#-1/4(1+2sqrt3)#

Explanation:

#"evaluating each of the trig. ratios"#

#sin210=-sin(210-180)=-sin30=-1/2#

#2cos210=2xx-cos(210-180)#

#color(white)(xxxxxx)=-2xxcos30=-2xxsqrt3/2=-sqrt3#

#sec300=1/cos300=1/cos(360-300)#

#color(white)(xxxxxxxxxxxx)=1/cos60=1/(1/2)=2#

#(sin210+2cos210)/sec300#

#=(-1/2-sqrt3)/2#

#=-1/4-1/2sqrt3=-1/4(1+2sqrt3)#

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