Find the exact value of cot &#x2061;<!--

Rapsinincke 2022-06-30 Answered
Find the exact value of cot ( 202.5 )
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Answers (2)

haingear8v
Answered 2022-07-01 Author has 13 answers
cot ( 202.5 0 ) = cot ( 180 0 + 22.5 0 ) = cot ( 22.5 0 )
Now Calculate value of tan ( 22.5 0 )
Using
tan ( 2 A ) = 2 tan A 1 tan 2 A ,
Put A = 22.5 0
We get
tan ( 45 0 ) = 2 tan ( 22.5 0 ) 1 tan 2 ( 22.5 0 ) 2 tan ( 22.5 0 ) = 1 tan 2 ( 22.5 0 )
So we get
tan 2 ( 22.5 0 ) + 2 tan ( 22.5 0 ) + 1 = 2 [ 1 + tan ( 22.5 0 ) ] 2 = ( 2 ) 2
So we get
1 + tan ( 22.5 0 ) = ± 2
So we get
tan ( 22.5 0 ) = 2 1
bcz tan ( 22.5 0 ) > 0
So we get
cot ( 22.5 0 ) = 1 tan ( 22.5 0 ) = 1 2 1 × 2 + 1 2 + 1 = 2 + 1
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Cristopher Knox
Answered 2022-07-02 Author has 6 answers
cot 202.5 0 = cot 22.5 , in third quadrant. Recognizing half of 45 0 you are going to need tan of half angle formula.
Denoting tan full angle by caps, T = 2 t 1 t 2 t = ( 1 + T 1 ) , tan 22.5 0 = 2 1 where we chose positive value from ± in third quadrant...and the required cot is its reciprocal:
cot 22.5 0 = 2 + 1.
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