Asked Sep 9, 2019

Simplify the expressions below.

(a) tan(cos−1 x)

(b) sin(tan−1 x)

Expert Answer

Step 1



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Let, => COS a X a COS X We know that sin2acos2a 1 sin2a 1 -cos2a => tV1-cos2a sin a = (cos a x) sin a = tan(cos x) tan a so, sin a COs a _ = + X

Step 2



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1 - x2 tan(cos x) X

Step 3



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1 X Let, tan a= x => a tan We know that sec2a 1tan2a sec2a tan2a = 1 => V1 tan2a => sec a = (tan a x) V1+x2 sec a= 1 1 (cosa => COS a= V1x2 sec a sin(tan x)sin a -1 so, = tan a cos a X


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