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Inverse Trigonometric Functions
Previous Year Questions (2022-2024)
Year 2022
- Find principal value of cos^{-1}(12) + 2sin^{-1}(12).
Show Solution
cos^{-1}(12) = π/3\nsin^{-1}(12) = π/6\nSum = π/3 + 2(π/6) = π/3 + π/3 = 2π/3 - Prove: tan^{-1}(12) + tan^{-1}(211) = tan^{-1}(34).
Show Solution
tan^{-1}a + tan^{-1}b = tan^{-1}(a+b1-ab)\n= tan^{-1}({1/2+2/111-1/11})\n= tan^{-1}({15/2210/11}) = tan^{-1}(34)
Year 2023
- Find principal value of cos^{-1}(12) + 2sin^{-1}(12).
Show Solution
cos^{-1}(12) = π/3\nsin^{-1}(12) = π/6\nSum = π/3 + 2(π/6) = π/3 + π/3 = 2π/3 - Prove: tan^{-1}(12) + tan^{-1}(211) = tan^{-1}(34).
Show Solution
tan^{-1}a + tan^{-1}b = tan^{-1}(a+b1-ab)\n= tan^{-1}({1/2+2/111-1/11})\n= tan^{-1}({15/2210/11}) = tan^{-1}(34)
Year 2024
- Find principal value of cos^{-1}(12) + 2sin^{-1}(12).
Show Solution
cos^{-1}(12) = π/3\nsin^{-1}(12) = π/6\nSum = π/3 + 2(π/6) = π/3 + π/3 = 2π/3 - Prove: tan^{-1}(12) + tan^{-1}(211) = tan^{-1}(34).
Show Solution
tan^{-1}a + tan^{-1}b = tan^{-1}(a+b1-ab)\n= tan^{-1}({1/2+2/111-1/11})\n= tan^{-1}({15/2210/11}) = tan^{-1}(34)