It is known that \sqrt{9-8\sin50^\circ}=a+b\sin c^\circ

Krystian Quintero

Krystian Quintero

Answered question

2022-02-28

It is known that
98sin50=a+bsinc

Answer & Explanation

surgescasjag

surgescasjag

Beginner2022-03-01Added 10 answers

We have the following (working in degrees):
cos20cos80=cos(5030)cos(50+30)=2sin50sin30=sin50
Thus we have that
12sin210sin10=sin50
(using cos20=12sin210 and cos80=sin(9080)=sin10)
And so
98sin50=98(12sin210sin10)=1+8sin10+16sin210=(1+4sin10)2
Thus a=1,b=4,c=10

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