If tan ß = nsin a cosa/ 1-n sin² a then tan (a - b) =
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Step-by-step explanation:
(1−n)tanA
We know that tan(A−B)=
1+tanAtanB
tanA−tanB
=
1+
cosA
sinA
×
1−nsin
2
A
nsinAcosA
cosA
sinA
−
1−nsin
2
A
nsinAcosA
=
cosA(1−nsin
2
A)
cosA−nsin
2
AcosA+nsin
2
AcosA
cosA(1−nsin
2
A)
sinA−nsin
3
A−nsinAcos
2
A
=
cosA
sinA−nsinA(sin
2
A+cos
2
A)
=
cosA
sinA−nsinA
=
cosA
(1−n)sinA
=(1−n)tanA
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