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Example 13 - Prove that sec A (1 - sin A)(sec A + tan A) = 1 - Examples

  1. Chapter 8 Class 10 Introduction to Trignometry
  2. Serial order wise
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Example 13 Prove that sec A (1 – sin A)(sec A + tan A) = 1. Solving L.H.S sec A (1 – sin A) (sec A + tan A) We write everything in terms of sin A and cos A = 1/cos⁡〖 𝐴〗 (1 – sin A) (" " 1/cos⁡〖 𝐴〗 +" " sin⁡〖 𝐴〗/cos⁡〖 𝐴〗 ) = ((1 −〖 sin〗⁡〖 𝐴)〗)/(cos⁡ 𝐴) (" " (1 +〖 sin〗⁡〖 𝐴〗)/cos⁡〖 𝐴〗 ) = ((1 −〖 sin〗⁡〖 𝐴) (1+〖 sin〗⁡〖 𝐴)〗 〗)/(cos⁡ 𝐴 × cos⁡〖 𝐴〗 ) We know that (a – b) (a + b) = a2 – b2 = ((12 −〖 sin2〗⁡〖 𝐴) 〗)/( cos⁡〖2 𝐴〗 ) = ((1 −〖 sin2〗⁡〖 𝐴) 〗)/( cos⁡〖2 𝐴〗 ) = (𝑐𝑜𝑠2 𝐴)/(cos2⁡ 𝐴) = 1 = R.H.S Thus, L.H.S = R.H.S Hence proved

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