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Most Important Selected Qs for JEE AdvancedMathematicsInverse Trigonometric Functions

In A B C , let a and b be minimum and maximum values of the function f(x)= ⁻¹ x+ ⁻¹ x+ ⁻¹ x respectively and A= 3 10 . If r= p q(q+ 10 ) where p, q are co-prime numbers, then find the value of (p+q) . [Note: Symbols used have usual meaning in A B C ]

Correct answer

7

Step-by-step solution

f(x)= ⁻¹ x+ ⁻¹ x+ ⁻¹ x Range of f(x)= [ 4 , 3 4 ] a= 4 and b= 3 4 Applying, A= b^2+c^2-a^2 2 b c 3 10 = 9 ^2 16 +c^2- ^2 16 2 ( 3 4 ) c c= 10 4 , 10 (rejected) Here, a^2+b^2=c^2 C=90^ r=(s-c) C 2 = ( + 10 4 2 - 10 4 ) 1= (4- 10 ) 8 = 6 8(4- 10 ) p q(q+ 10 ) p=3 and q=4 p+q=7

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