Ex 2.2, 7 - Chapter 2 Class 12 Inverse Trignometry - tan-1 - Ex 2.2

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.2, 7 Write the function in the simplest form: tan-1 (√((1 −〖 cos〗⁡x)/(1 +〖 cos〗⁡x ))), x < π Lets first calculate value of 1 – cos x & 1 + cos x tan-1 (√((1 −〖 cos〗⁡x)/(1 +〖 cos〗⁡x ))) = tan-1 (√((2 sin2 x/2 )/(2 cos2 x/2))) = tan-1 (√((sin2 x/2 )/(cos2 x/2))) = tan-1 (√(tan2⁡〖 𝑥/2〗 )) = tan-1 (tan⁡〖 𝑥/2〗 ) = 𝑥/2 Hence, tan-1 (√((1 −〖 cos〗⁡x)/(1 +〖 cos〗⁡x ))) = 𝑥/2

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