How do you simplify $(1+tantheta)/(1+cottheta)$ ?

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Answer 1 · 2018-08-01T04:56:11

$(1+tantheta)/(1+cottheta)=tantheta$

Here,

$(1+tantheta)/(1+cottheta)=(1+tantheta)/(1+1/tantheta)to[becausecottheta=1/tantheta]$

$=>(1+tantheta)/(1+cottheta)= (1+tantheta)/((tantheta+1)/tantheta)$

$=>(1+tantheta)/(1+cottheta)=tantheta((1+tantheta)/(tantheta+1))$

$:.(1+tantheta)/(1+cottheta)=tantheta$

Answer 2 · 2018-08-01T06:04:03

$color(purple)(=> sin theta / cos theta = tan theta$

$(1 + tan theta) / (1 + cot theta)$

$=> (1 + sin theta/cos theta) / (1 + cos theta / sin theta)$

$=> (cancel(cos theta + sin theta)/cos theta) / (cancel(sin theta + cos theta)/sin theta)$

$color(purple)(=> sin theta / cos theta = tan theta$

How do you simplify (1+tantheta)/(1+cottheta)(1+tantheta)/(1+cottheta)?