RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12th

Q. No. 11 of Exercise 4.14

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11

For any a,b,x,y>0, prove that:

, where a=-ax by, β = bx + ay.

Given:-


Take


LHS


=


Dividing numerator and denominator of 1st term and 2nd term by b3 and y3 respectively.


=


=


We know that, Formula



Thus,


=


=


=


We know that, Formula



Thus,


=


=


=


As given,


ay + bx =β, -ax + by = α


=


We know that, Formula



Thus,


=


=


=


= RHS


So,



Hence Proved


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