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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.