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Ex 2.2, 8 - Chapter 2 Class 12 Inverse - tan-1 (cos x - sin x) - Ex 2.2

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  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.2, 8 Write the function in the simplest form: tan-1 (cos⁡〖x − sin⁡x 〗/cos⁡〖x + sin⁡x 〗 ), 0< x < π tan-1 (cos⁡〖x − sin⁡x 〗/cos⁡〖x + sin⁡x 〗 ) Dividing cos x inside = tan-1 (((cos⁡𝑥 − sin⁡x)/cos⁡𝑥 )/((cos⁡𝑥 + sin⁡x)/cos⁡𝑥 )) = tan-1 (((cos x)/cos⁡〖x 〗 − (sin x)/cos⁡〖x 〗 )/((cos x)/cos⁡〖x 〗 + (sin x)/cos⁡〖x 〗 )) = tan-1 ((1 − tan⁡x)/(1 +〖 tan〗⁡x )) = tan-1 ((1 − tan⁡x)/(1 +〖 1 . tan〗⁡x )) = tan-1 ((tan⁡〖 𝜋/4〗 − tan⁡𝑥)/(1 + tan⁡〖𝜋/4 .〖 tan〗⁡𝑥 〗 )) = tan-1 (tan (𝜋/4 −𝑥)) = 𝜋/4 − x

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