Q. 634.5( 11 Votes )

# If <img wid

Answer :

Given: Put x = sin α and y = sin β …(i)  Now, we know that sin2θ + cos2 θ = 1 cos α + cos β = a( sin α – sin β) …(ii)

Now, we use some trigonometry formulas,  So, eq.(ii) become     2 cot-1 a = α – β …(iii)

Now, from eq.(i), we have

α = sin-1 x and β = sin-1 y

Now, put value of α and β in eq. (iii), we get

2 cot-1 a = sin-1 x – sin-1 y

or sin-1 x – sin-1 y = 2cot-1 a

On differentiating above with respect to x, we get    Hence Proved

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 :

Show that of all Mathematics - Board Papers

Find the value ofMathematics - Board Papers

If x sin (a + y) Mathematics - Exemplar

The function f(x)Mathematics - Exemplar

Show that of all Mathematics - Board Papers

If the function fMathematics - Board Papers

Find <img wMathematics - Exemplar

Let f(x) = |sinx|Mathematics - Exemplar

The derivative ofMathematics - Exemplar