Respuesta :
Tan is zero when sin is zero. So, inverse tan of zero will be zero (or 180 degrees or 360 degrees or multiples of such). And, sin of any of those will be zero. So, the answer must be zero.
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Answer:
The value of the expression:
Sin ( Tan^-1 (0))=0
Step-by-step explanation:
We are asked to evaluate the expression:
[tex]\sin(\tan^{-1}(0))[/tex]
we know that :
[tex]\tan(0)=0[/tex]
since,
[tex]\tan x=\dfrac{\sin x}{\cos x}[/tex]
and we know that:
[tex]\sin (0)=0\\\\Hence,\\\\\tan (0)=0[/tex]
Hence,
[tex]\sin(\tan^{-1}(0))=\sin(\tan^{-1}\tan(0))\\\\\\\sin(\tan^{-1}(0))=\sin(0)[/tex]
since, the composition of tan and it's inverse is identity.
Also,
[tex]\sin(n\pi)=0[/tex] where n belongs to integers.
Hence,
[tex]\tan(n\pi)=0[/tex]
Hence, we get:
[tex]\sin(\tan^{-1}(0))=0[/tex]
Since, [tex]\sin(\tan^{-1}(0))=\sin(\tan^{-1}\tan(n\pi))=\sin(n\pi)=0[/tex]
Hence,the answer is:
0
