Q. 14.0( 3 Votes )

Find the principa

Answer :

Let us understand what principal value of inverse trigonometric function is.

The principal value of an inverse trigonometric function, say, cos-1 x for x > 0, is the length of the arc of a unit circle centred at the origin which subtends an angle at the centre whose cosine is x. For this reason cos-1 x is also denoted by arc cos x.


First, let us find principal value of . Let the principal value be x, such that




Note that, . So,



Range of principal value of sin-1 is between and .


And, .


Hence, principal value of is .


Now, let is find principal value of . Let the principal value be y, such that




Note that, . So,



Since, range of principal value of cos-1 is between 0 and π.


And, does not belong to [0, π].


So,






Hence, principal value of is .


Now, add the principal values.






Thus, principal value of is .


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