Question

Calcular o Sen 75º ( 30º + 45º) ?

Answer 1

$\boxed{\boxed{sen~(a+b)=sen~a\cdot cos~b+sen~b\cdot cos~a}}$
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$sen(75\º)=sen(30\º+45\º)\\\\sen(75\º)=sen(30\º)\cdot cos(45\º)+sen(45\º)\cdot cos(30\º)\\\\sen(75\º)=\frac{1}{2}\cdot\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2}\\\\sen(75\º)=\frac{\sqrt{2}}{4}+\frac{\sqrt{2\cdot3}}{4}\\\\\\\boxed{\boxed{sen(75\º)=\dfrac{\sqrt{2}+\sqrt{6}}{4}}}$