\tan\left(t+\pi\right)=___, and \cot\left(t+\pi\right)=___, so the t

DofotheroU

DofotheroU

Answered question

2021-09-10

tan(t+π)=___, and cot(t+π)=___, so the tangent and cotangent functions are___functions.The period of each of these functions is___.

Answer & Explanation

Bella

Bella

Skilled2021-09-11Added 81 answers

Step 1
Given
tan(t+π)=___, and cot(t+π)=___, so the tangent and cotangent functions are___functions.The period of each of these functions is___.
Step 2
Use the identity: tan(x)=sin(x)cos(x)
tan(t+π)=sin(t+π)cos(t+π)
Use the identities
sin(s+t)=cos(s)sin(t)+cos(t)sin(s)
cos(s+t)=cos(s)cos(t)+sin(s)sin(t)
=cos(t)sin(π)+cos(π)sin(t)cos(t)cos(π)+sin(t)sin(π)
=sin(t)cos(π)cos(t)sin(π)sin(t)
=sin(t)cos(t)
=tan(t)
tan(t+π)=tant
tan(t+π)=tan(t) thus tangent function is periodic function with period x.
Step 3
Use the identity:cot(x)=cos(x)sin(x)
cot(t+π)=cos(t+π)sin(t+π)
Use the identities :
sin(s+t)=cos(s)sin(t)+cos(t)sin(s)
cos(s+t)=cos(s)cos(t)+sin(s)sin(t)

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