How do you find the exact value of tan(cos^-1(sqrt2/2))

sarahkobearab4

sarahkobearab4

Answered question

2022-08-11

How do you find the exact value of tan ( cos 1 ( 2 2 ) )?

Answer & Explanation

raffatoaq

raffatoaq

Beginner2022-08-12Added 22 answers

Recall the Defn. :-
cos 1 x = θ , | x | 1 x = cos θ , θ [ 0 , π ]
Knowing that, cos ( π 4 ) = 2 2 , π 4 [ 0 , π ] ; cos 1 ( 2 2 ) = π 4
Hence,
tan { cos 1 ( 2 2 ) } = tan ( π 4 ) = 1

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