You can put this solution on YOUR website! please help me find the exact value of 6(cos105degree)(sin45degree
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cos(105˚)=cos(60+45)=cos60*cos45-sin60sin45=1/2*√2/2-√3/2*√2/2=√2/4-√6/4=(√2-√6)/4
sin45˚=√2/2
6(cos105degree)(sin45degree)=6(√2-√6)/4*√2/2=6(√4-√12)/8=6*2(1-√3)/8=(3/2)(1-√3)
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calculator check:
6cos105˚*sin45˚≈-1.098…
Exact value as calculated=(3/2)(1-√3)≈-1.098…
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