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 .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Prove the followiMathematics - Board Papers

Solve the followiMathematics - Board Papers