Question

qual o valor y, se y=cos 75° + cos 15°?

Answer 1

y=Cos(75)+Cos(15)

Cos(75)=Cos(45+30)

Cos(45+30)=Cos(45)Cos(30)-sen(45)Sen(30)

=√2/2×√3/2 - √2/2×1/2

=√6-√2/4

Cos(15)=Cos(45-30)=√6+√2/4

y=(√6-√2/4)+(√6+√2/4)

y=2√6/4

[y=√6/2]

$\boxed{ \boxed{ \boxed{\mathrm{y = \frac{ \sqrt{6} }{2}}}}}$

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Answer 2

Resposta:

y=√6/2

Explicação passo-a-passo:

y=cos75°+cos15°

y=cos(45°+30°)+cos(45°-30°)

Identidades:

cos(a+b)=cosacosb-senasenb

cos(a-b)=cosacosb+senasenb

y=cos45°cos30°-sen45°sen30°+[cos45°cos30°+sen45°sen30°]

y=2cos45°cos30°

y=2(√2/2)(√3/2)

y=√2.√3/2

y=√6/2