Negative, reciprocal and complementary arguments

JEE Main Mathematics · Inverse Trigonometric Functions · 3 questions, latest first

• Let the maximum value of ( sin^-1 x)^2+( cos^-1 x)^2 for x ∈[-(√3)/2, 1/(√2)] be m/n π^2, where gcd(m, n)=1. Then m+n is equal to…202621 January, Shift 2 · Q23
• Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of 16(( sec^-1…202522 January, Shift 1 · Q14
• Let (a, b) ⊂(0,2 π) be the largest interval for which sin^-1( sin θ)- cos^-1( sin θ)>0, θ ∈(0,2 π), holds. If α x^2+β x+…202331 January, Shift 2 · Q78