Inverse trigonometric equations

JEE Main Mathematics · Inverse Trigonometric Functions · 11 questions, latest first

• If k= tan ((π)/4+1/2 cos^-1(2/3))+ tan (1/2 sin^-1(2/3)), then the number of solutions of the equation sin^-1(k x-1)= sin^-1 x-…202628 January, Shift 1 · Q22
• The number of solutions of tan^-1 4 x+ tan^-1 6 x=(π)/6, where -1/(2 √6)<x<1/(2 √6), is equal to202622 January, Shift 1 · Q12
• Let S={x: cos^-1 x=π+ sin^-1 x+ sin^-1(2 x+1)}. Then Σ_x ∈ S(2 x-1)^2 is equal to ____.202529 January, Shift 1 · Q23
• Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 sin^-1 x+3 cos^-1…20249 April, Shift 2 · Q30
• Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying…202427 January, Shift 2 · Q20
• For x ∈(-1,1], the number of solutions of the equation sin^-1 x=2 tan^-1 x is equal to ____.202313 April, Shift 2 · Q30
• If S={x ∈ R: sin^-1((x+1)/(√(x^2+2 x+2)))- sin^-1(x/(√(x^2+1)))=(π)/4}, then Σ_x ∈ s( sin ((x^2+x+5) (π)/2)- cos ((x^2+x+5) π))…202313 April, Shift 1 · Q30
• Let S={x ∈ R: 0<x<1. and.2 tan^-1((1-x)/(1+x))= cos^-1((1-x^2)/(1+x^2))}. If n(S) denotes the number of elements in S then:20231 February, Shift 2 · Q79
• Let S be the set of all solutions of the equation cos^-1(2 x)-2 cos^-1(√(1-x^2))=π, x ∈[-1/2, 1/2]. Then Σ_x ∈ S 2 sin^-1(x^2-1)…20231 February, Shift 1 · Q79
• Let y=f(x) represent a parabola with focus (-1/2, 0) and directrix y=-1/2. Then S={x ∈ R: tan^-1(√(f(x)))+…202331 January, Shift 1 · Q75
• If the sum of all the solutions of tan^-1((2 x)/(1-x^2))+ cot^-1((1-x^2)/(2 x))=(π)/3,-1<x<1, x ≠ 0, is α-4/(√3), then α is equal…202325 January, Shift 1 · Q90