Simplify without using tables or calculations {Sin²315°(1-tan²210°)}÷{(1+cos²120°)(1+tan²330°)}?

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Answer 1 · 2018-01-08T17:08:03

#{sin²315°(1-tan²210°)}÷{(1+cos²120°)(1+tan²330°)}=1/5#

#sin315^@=sin(360^@-45^@)=-sin45^@=-1/sqrt2#

#tan210^@=tan(180^@+30^@)=tan30^@=1/sqrt3#

#cos120^@=cos(180^@-60^@)=-cos60^@=-1/2#

and #tan330^@=tan(360^@-30^@)=-tan30^@=-1/sqrt3#

#{sin²315°(1-tan²210°)}÷{(1+cos²120°)(1+tan²330°)}#

= #((-1/sqrt2)^2(1-(1/sqrt3)^2)-:((1+(-1/2)^2)(1+(-1/sqrt3)^2)#

= #1/2(1-1/3)-:((1+1/4)(1+1/3))#

= #(1/2xx2/3)-:(5/4xx4/3)#

= #1/3-:5/3#

= #1/3xx3/5#

= #1/5#