Sum and difference formulae

JEE Main Mathematics · Inverse Trigonometric Functions · 7 questions, latest first

• Let 0<α<1, β=1/(3 α) and tan^-1(1-α)+ tan^-1(1-β)=(π)/4. Then 6(α+β) is equal to:20266 April, Shift 1 · Q13
• Considering the principal values of the inverse trigonometric functions, sin^-1((√3)/2 x+1/2 √(1-x^2)),-1/2<x<1/(√2), is equal to20254 April, Shift 1 · Q13
• cos ( sin^-1 3/5+ sin^-1 5/13+ sin^-1 33/65) is equal to:202528 January, Shift 1 · Q13
• If α>β>γ>0, then the expression cot^-1{β+((1+β^2))/((α-β))}+ cot^-1{γ+((1+γ^2))/((β-γ))}+ cot^-1{α+((1+α^2))/((γ-α))} is equal to:202524 January, Shift 2 · Q14
• For n ∈ N, if cot^-1 3+ cot^-1 4+ cot^-1 5+ cot^-1 n=(π)/4, then n is equal to ____.20246 April, Shift 1 · Q30
• Given that the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [-1,1] such that…20244 April, Shift 2 · Q20
• For α, β, γ ≠ 0, if sin^-1 α+ sin^-1 β+ sin^-1 γ=π and (α+β+γ)(α-γ+β)=3 α β, then γ equals202431 January, Shift 1 · Q20