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There are some standard substitutions, where we put value of x and solve it
Inverse Trigonometry Substitution
Last updated at August 13, 2026 by Teachoo
Not clear how to approach
Chapter 2 Class 12 Inverse Trigonometric Functions
Concept wise
- Definition
- Finding principal value
- Formulae based
- Changing of trignometric variables and then applying formula
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Not clear how to approach
Transcript
Sometimes while integrating, We get questions like ∫1▒√(𝑎^2−𝑥^2 ) 𝑑𝑥 Now, how do we solve it? There are some standard substitutions, where we put value of x and solve it √(𝑎^2−𝑥^2 ) 𝑥=𝑎 𝑠𝑖𝑛𝜃 1−〖𝑠𝑖𝑛〗^2𝜃=〖𝑐𝑜𝑠〗^2𝜃 √(𝑎^2+𝑥^2 ) 𝑥=𝑎 𝑡𝑎𝑛𝜃 1+〖𝑡𝑎𝑛〗^2𝜃=〖𝑠𝑒𝑐〗^2𝜃 √(𝑥^2−𝑎^2 ) 𝑥=𝑎 𝑠𝑒𝑐𝜃 〖𝑠𝑒𝑐〗^2𝜃−1=〖𝑡𝑎𝑛〗^2𝜃
