Question 9: Find the principal value of cos¯¹(-1/√2)
Class 12 - Math - Inverse Trigonometric Functions
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Let cos-1 (- 1 /√2 ) = ∅,
then cos ∅= - 1 /√2
= -cos ( π /4 ) = cos (π- π /4 )
= cos ( 3π /4 ).
We know that the range of the principal value branch of cos−¹is [0, π] and cos ( 3π /4 ) = - 1 √2
Therefore,
the principal value of cos-¹ (- 1/√2 ) is 3π /4
then cos ∅= - 1 /√2
= -cos ( π /4 ) = cos (π- π /4 )
= cos ( 3π /4 ).
We know that the range of the principal value branch of cos−¹is [0, π] and cos ( 3π /4 ) = - 1 √2
Therefore,
the principal value of cos-¹ (- 1/√2 ) is 3π /4
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