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Simplify the expressions below.(a) tan(cos-1 x)(b) sin(tan1 x)

Question
Simplify the expressions below.
(a) tan(cos-1 x)
(b) sin(tan1 x)
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Simplify the expressions below. (a) tan(cos-1 x) (b) sin(tan1 x)

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Step 1

Refer to the question.

Let a = cos^(-1) x.  That is from the properties of inverse trigonometric,

a cosx
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a cosx

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Step 2

Now tan(cos^(-1) x)= tan(a)

sin a
tan a
cos a
Also sin2 a+cos2 a 1
sin a1-cos2 a
tan a
tan(cos= V1-r
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sin a tan a cos a Also sin2 a+cos2 a 1 sin a1-cos2 a tan a tan(cos= V1-r

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Step 3

Now for part b sin(...

sin (tan x
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sin (tan x

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