Composition of trigonometric and inverse functions

JEE Main Mathematics · Inverse Trigonometric Functions · 10 questions, latest first

• If sin ( tan^-1(x √2))= cot ( sin^-1 √(1-x^2)), x ∈(0,1), then the value of x is:20266 April, Shift 2 · Q13
• Considering the principal values of inverse trigonometric functions, the value of the expression tan (2 sin^-1(2/(√13))-2…202628 January, Shift 2 · Q11
• The value of cot^-1((√(1+ tan^2(2))-1)/(tan (2)))- cot^-1((√(1+ tan^2(1/2))+1)/(tan (1/2))) is equal to20258 April, Shift 2 · Q13
• If y= cos ((π)/3+ cos^-1 x/2), then (x-y)^2+3 y^2 is equal to ____.20252 April, Shift 2 · Q23
• If for some α, β; α ≤ β, α+β=8 and sec^2( tan^-1 α)+cosec^2( cot^-1 β)=36, then α^2+β is ____.202524 January, Shift 1 · Q24
• If (π)/2 ≤ x ≤ (3 π)/4, then cos^-1(12/13 cos x+5/13 sin x) is equal to202523 January, Shift 1 · Q10
• The integral ∫_1 / 4^3 / 4 cos (2 cot^-1 √((1-x)/(1+x))) d x is equal to20249 April, Shift 2 · Q11
• If a= sin^-1( sin (5)) and b= cos^-1( cos (5)), then a^2+b^2 is equal to202431 January, Shift 2 · Q20
• Let x=m/n ( m, n are co-prime natural numbers) be a solution of the equation cos (2 sin^-1 x)=1/9 and let α, β(α>β) be the roots…202429 January, Shift 2 · Q19
• If sin^-1 (α)/17+ cos^-1 4/5- tan^-1 77/36=0,0<α<13, then sin^-1( sin α)+ cos^-1( cos α) is equal to202331 January, Shift 1 · Q79