Evaluate sin105° using the sum and differences identities underdstanding 105°=45°+60°

1 answer:

7 0

$\bf \textit{Sum and Difference Identity}
\\\\
sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\\\\
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sin(45^o+60^o)\implies sin(45^o)cos(60^o)+cos(45^o)sin(60^o)
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\cfrac{\sqrt{2}}{2}\cdot \cfrac{1}{2}+\cfrac{\sqrt{2}}{2}\cdot \cfrac{\sqrt{3}}{2}\implies \cfrac{\sqrt{2}}{4}+\cfrac{\sqrt{6}}{4}\implies \cfrac{\sqrt{2}+\sqrt{6}}{4}$

check your Unit Circle for those angles.

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