# 8 - Inverse Trigonometry Questions Answers

**Asked By: PRIKSHIT**4 year ago

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if [cot‾1 x]+[cos‾1 x] =0 then complete set of values of x is

**Asked By: HARSHITA JAISWAL**4 year ago

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value of ∑cot^-1(x^4+x^2+2/2x) is (note summation vary from x=0to x=0∞)

**Asked By: AMIT**4 year ago

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If sin^{-1}[2p / 1+p^{2} ] - cos^{-1}[1-q^{2 }/ 1+q^{2]}] = tan^{-1}[2x / 1-x^{2}] , prove that x = p-q / 1+pq ,where p,q belongs to (0,1)

**Asked By: SHRISHTI**5 year ago

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sin‾¹(sin2) + sin‾¹(sin4) + sin‾¹(sin6) = ?

**Asked By: BONEY HAVELIWALA**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

sin‾¹(sin2) + sin‾¹(sin4) + sin‾¹(sin6)

= (π-2) + (π-4) + (6-2π)

= 0

**If cos ^{-1}x - cos^{-1}(y/2) = α , then 4x^{2}-4xycosα + y^{2} is equal to ?**

**Asked By: AMIT DAS**7 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

according to the given condition

cos^{-1}x = cos^{-1}(y/2) + a

so x = cos ( cos^{-1}y/2 + a)

so x = y/2 cosa - sin cos^{-1}y/2 + sina

so x = y/2 cosa - [1-(y^{2}/4)]^{1/2} + sina

so x - sina - y/2 cosa = -[1-(y^{2}/4)]^{1/2}

now square both side and solve

If sin^{-1}a + sin^{-1}b+ sin^{-1}c = π , then the value of { a√(1-a^{2}) + b√(1-b^{2}) + c√(1-c^{2})}

**Asked By: AMIT DAS**7 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

let sin^{-1}a = A , sin^{-1}b = B and sin^{-1}c= C^{ }

so ^{ }{ a√(1-a^{2}) + b√(1-b^{2}) + c√(1-c^{2})} = sinAcosA + sinBcosB + sinCcosC = 1/2 (sin2A+sin2B+sin2C)

= 1/2 (4sinAsinBsinC)

= 2abc

If [cot‾^{1}x] + [cos‾^{1}x] = 0 , then complete set of value of x is ( [ * ] is GIF)?

**Asked By: AMIT DAS**7 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

These are the graphs for cot^{-1}x and cos^{-1}x

violet for cos and green for cot

from graph it is clear that cos part with integer function will be 0 for cos1<x≤1

and cot part with integer function will be 0 for cot1<x<∞

so answer will be cot1<x≤1