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Mathematics
Mathematics
Problem
66. Practicing for Calculus Express each of the following functions as an algebraic expression involving no trig functions. (a)
cos
(
sin
−
1
2
x
)
\cos \left(\sin ^{-1} 2 x\right)
cos
(
sin
−
1
2
x
)
(b)
sec
2
(
tan
−
1
x
)
\sec ^{2}\left(\tan ^{-1} x\right)
sec
2
(
tan
−
1
x
)
(c)
sin
(
cos
−
1
x
)
\sin \left(\cos ^{-1} \sqrt{x}\right)
sin
(
cos
−
1
x
)
(d)
−
csc
2
(
cot
−
1
x
)
-\csc ^{2}\left(\cot ^{-1} x\right)
−
csc
2
(
cot
−
1
x
)
(e)
tan
(
sec
−
1
x
2
)
\tan \left(\sec ^{-1} x^{2}\right)
tan
(
sec
−
1
x
2
)
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