find range
y= sinx(sin³x+3)+cox(cos³x+4)+sin²(2x)+4cosx+5
Answers
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Answer:
p(x)=sin
4
(x)+3sin(x)+cos
4
(x)+4cos(x)+2sin
2
(x).cos
2
(x)+5
=(sin
4
(x)+cos
4
(x)+2sin
2
(x).cos
2
(x))+5(
5
4cos(x)
+
5
3sin(x)
)+5
=(sin
2
(x)+cos
2
(x))
2
+5cos(x−37
0
)+5
=1+5(1+cos(x−37
0
))
Where cos37
0
=
5
4
Hence
1+5(1+cos(x−37
0
))
=1+5(2cos
2
(
2
x−37
0
))
p(x)=1+10cos
2
(
2
x−37
0
)
Now
0≤cos
2
(
2
x−37
0
)≤1
Hence
1≤p(x)≤11
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