Inverse Trigonometric Functions questions
371 published questions with worked solutions.
- Given the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [−1, 1] such that...
- If the domain of the function ^ -1 ( 3x - 22 2x - 19 ) + _e ( 3x^2 - 8x + 5 x^2 - 3x - 10 ) is (α, β], then 3α + 10β is equal to-
- For n ∈ N, if cot⁻¹3 + cot⁻¹4 + cot⁻¹5 + cot⁻¹n = 4, then n is equal to ____.
- Let f(x)=( ( ^ -1 x)+ ( ^ -1 x))^2-1, |x| > 1. If dy dx = 1 2 d dx ( ^ -1 (f(x))) and y( 3 )= 6 , then y(- 3 ) is equal to -
- If y= _ k=1 ^ 6 k ^ -1 3 5 kx- 4 5 kx , then dy dx at x = 0 is ___________.
- The domain of the function f(x)= ^ -1 ( |x|+5 x^2+1 ) is (- ,-a] [a, ). Then a is equal to:
- 2 - ( ^ -1 4 5 + ^ -1 5 13 + ^ -1 16 65 ) is equal to-
- Is S is the sum of the first 10 terms of the series ^ -1 ( 1 3 )+ ^ -1 ( 1 7 )+ ^ -1 ( 1 13 )+ ^ -1 ( 1 21 )+ , then tan(S) is...
- If x_1,x_2,x_3,x_4 are roots of the equation x^4-x^3 2 +x^2 2 -x - =0, then ^ -1 x_1+ ^ -1 x_2+ ^ -1 x_3+ ^ -1 x_4 is equal to
- If , are the roots of the equation 6x^2-5x+1=0, then the value of ^ -1 + ^ -1 is
- Let [·] denote the greatest integer function. If the domain of the function f(x) = ^ -1 ( 4x+2[x] 3 ) is [α, β], then 12(α + β)...
- If y = ^ -1 ( 3 x - 4 x 4 x + 3 x ) + 2 ^ -1 ( x 1+ 1-x^2 ), then dy dx at x = 3 2 is equal to:
- If 4+ _ p=1 ^ 11 ^ -1 ( 2^ p-1 1+2^ 2p-1 )= , then tanα is equal to _______.
- If ( ^ -1 (x 2))= ( ^ -1 1-x^2 ), x∈(0,1), then the value of x is:
- Let [·] denote the greatest integer function. If the domain of the function f(x)= ^ -1 ( x+[x] 3 ) is [α, β], then α²+β² is equal...
- Let 0<α<1, β=1/(3α) and tan⁻¹(1−α)+tan⁻¹(1−β)=π/4. Then 6(α+β) is equal to:
- Let α = 3 sin⁻¹(6/11) and β = 3 cos⁻¹(4/9), where inverse trigonometric functions take only the principal values. Given below are...
- The integral _ 1/4 ^ 3/4 (2 ^ -1 1-x 1+x )dx is equal to :
- Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 sin⁻¹x + 3 cos⁻¹x =...
- If the domain of the function f(x) = ^ -1 ( x-1 2x+3 ) is ℝ − (α, β] then 12αβ is equal to
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