if b= 3√2,a=3,A=30 degrees, then B=?
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Answer:
First of all, from the basic rules of trigonometry, sin\thetasinθ or cos\thetacosθ have a maximum value of 1.
Therefore, in order for sin3a+cos2bsin3a+cos2b to be equals to 2, this means that both 'sin3a' and 'cos2b' have reached their maximum value of 1.
Hence,
\begin{gathered}sin3a=1\:\:\:and\:\:\:cos2b=1\\3a=90^o\:\:\:\:and\:\:\:\:2b=0^o\\a=30^o\:\:\:\:\:and\:\:\:\:b=0^o\end{gathered}
sin3a=1andcos2b=1
3a=90
o
and2b=0
o
a=30
o
andb=0
o
Now, we need to evaluate:
\begin{gathered}cos2a+sin3b\\=cos2(30^o)+sin3(0^o)\\=cos60^o+sin0^o\\=\frac{1}{2}\end{gathered}
cos2a+sin3b
=cos2(30
o
)+sin3(0
o
)
=cos60
o
+sin0
o
=
2
1
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