Example 10 - Chapter 8 Class 10 Introduction to Trignometry

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Example 10 - Prove that sec A (1 - sin A)(sec A + tan A) = 1 - Examples

part 2 - Example 10 - Examples - Serial order wise - Chapter 8 Class 10 Introduction to Trignometry

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Example 10 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) Writing everything in terms of sin A and cos A = 1/cos⁑〖 𝐴〗 (1 – sin A) (" " 1/cos⁑〖 𝐴〗 +" " sin⁑〖 𝐴〗/cos⁑〖 𝐴〗 ) = ((1 βˆ’γ€– sin〗⁑〖 𝐴)γ€—)/(cos⁑ 𝐴) (" " (1 +γ€– sin〗⁑〖 𝐴〗)/cos⁑〖 𝐴〗 ) = ((𝟏 βˆ’γ€– π’”π’Šπ’γ€—β‘γ€– 𝑨) (𝟏+γ€– π’”π’Šπ’γ€—β‘γ€– 𝑨)γ€— γ€—)/(𝒄𝒐𝒔⁑ 𝑨 Γ— 𝒄𝒐𝒔⁑〖 𝑨〗 ) Since (a – b) (a + b) = a2 – b2 = ((12 βˆ’γ€– sin2〗⁑〖 𝐴) γ€—)/( cos⁑〖2 𝐴〗 ) = ((𝟏 βˆ’γ€– π¬π’π§πŸγ€—β‘γ€– 𝑨) γ€—)/( π’„π’π’”β‘γ€–πŸ 𝑨〗 ) = (π’„π’π’”πŸ 𝑨)/(𝐜𝐨𝐬𝟐⁑ 𝑨) = 1 = R.H.S Thus, L.H.S = R.H.S Hence proved cos2 A + sin2 A = 1 cos2 A = 1 – sin2 A 1 – sin2 A = cos2 A

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