How to use a half-angle formula to simplify tan[(7pi)/8 ]?

pacheclownfgtv

pacheclownfgtv

Answered question

2023-03-23

How to use a half-angle formula to simplify tan [ 7 π 8 ] ?

Answer & Explanation

peminggirotnn

peminggirotnn

Beginner2023-03-24Added 5 answers

Put the trig identity to use: tan 2 x = 1 - cos 2 x 1 + cos 2 x
tan 2 ( 7 π 8 ) = 1 - cos ( 7 π ) 4 1 + cos ( 7 π ) 4 =
or cos ( 7 π 4 ) = cos ( π 4 ) = 1 2 , then:
tan 2 ( 7 π 8 ) = 2 - 1 2 + 1 =
= ( 2 - 1 ) 2 2 - 1 = ( 2 - 1 ) 2
Finally, tan ( 7 π 8 ) = ( 2 - 1 )

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