triangle ZAT, AZ = AT and AE bisects ∠ZAT. If ∠T = 65⁰, then find the value of ∠ZAE.
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Answer:
Given that, \frac{b-c}{b+c}cot(\frac{A}{2}) + \frac{b+c}{b-c}tan(\frac{A}{2} ) = 2
b+c
b−c
cot(
2
A
)+
b−c
b+c
tan(
2
A
)=2
=> tan(\frac{B-C}{2} )+ \frac{1}{tan(\frac{B-C}{2}) } = 2tan(
2
B−C
)+
tan(
2
B−C
)
1
=2
=> tan^{2}(\frac{B-C}{2})+1=2tan(\frac{B-C}{2} )tan
2
(
2
B−C
)+1=2tan(
2
B−C
)
=> tan^{2} (\frac{B-C}{2})-2 tan(\frac{B-C}{2}) +1=0tan
2
(
2
B−C
)−2tan(
2
B−C
)+1=0
=> (tan(\frac{B-C}{2}) -1)^{2}=0(tan(
2
B−C
)−1)
2
=0
=> tan(\frac{B-C}{2}) = 1tan(
2
B−C
)=1
=> B-C = \frac{\pi}{2}B−C=
2
π
Therefore, it is not possible to say about the type of triangle.
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