Slide26.JPG

Slide27.JPG
Slide28.JPG

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


Transcript

Ex 8.3, 4 Prove the following identities, where the angles involved are acute angles for which the expressions are defined. "cos A – sin A + 1" /"cos A + sin A – 1" = cosec A + cot A, using the identity cosec2 A = 1 + cot2 A. Solving L.H.S (cos⁑𝐴 βˆ’ sin⁑𝐴 + 1)/(cos⁑𝐴 + sin⁑𝐴 βˆ’ 1) Since we need to use cosec and cot identity Dividing both numerator and denominator by sin A = (𝟏/π’”π’Šπ’β‘γ€– 𝑨〗 (cos⁑〖 𝐴 βˆ’ sin⁑〖𝐴 + 1γ€— γ€— ))/(𝟏/π’”π’Šπ’β‘γ€– 𝑨〗 (cos⁑〖 𝐴 + sin⁑〖 𝐴 βˆ’ 1γ€— γ€— ) ) = (cos⁑〖 𝐴〗/sin⁑〖 𝐴〗 βˆ’ sin⁑〖 𝐴〗/sin⁑〖 𝐴〗 + 1/sin⁑〖 𝐴〗 )/(cos⁑〖 𝐴〗/sin⁑〖 𝐴〗 + sin⁑〖 𝐴〗/sin⁑〖 𝐴〗 βˆ’ 1/sin⁑〖 𝐴〗 ) = cot⁑〖 𝐴 βˆ’ 1 + π‘π‘œπ‘ π‘’π‘ 𝐴〗/cot⁑〖 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴〗 = ((cot⁑〖 𝐴 + π‘π‘œπ‘ π‘’π‘ 𝐴) βˆ’ πŸγ€—)/((cot⁑〖 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴) γ€— ) = ((co𝑑⁑〖 𝐴 + π‘π‘œπ‘ π‘’π‘ 𝐴) βˆ’ (π’„π’π’”π’†π’„πŸ 𝑨 βˆ’ π’„π’π’•πŸ 𝑨)γ€—)/((cot⁑ 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴)) = ((co𝑑⁑〖 𝐴 + π‘π‘œπ‘ π‘’π‘ 𝐴) βˆ’ (πœπ¨π’”π’†π’„β‘π‘¨ βˆ’ 𝒄𝒐𝒕 𝑨)(πœπ¨π’”π’†π’„β‘π‘¨ + 𝒄𝒐𝒕 𝑨)γ€—)/((cot⁑ 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴)) = ((co𝑑⁑〖 𝐴 + π‘π‘œπ‘ π‘’π‘ 𝐴) [𝟏 βˆ’ (𝒄𝒐𝒔𝒆𝒄 𝑨 βˆ’ 𝒄𝒐𝒕 𝑨 )]γ€—)/([cot⁑ 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴]) = ((co𝑑⁑〖 𝐴 + π‘π‘œπ‘ π‘’π‘ 𝐴) [1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴 + π‘π‘œπ‘‘ 𝐴]γ€—)/([cot⁑ 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴]) = ((co𝑑⁑〖 𝐴 + π‘π‘œπ‘ π‘’π‘ 𝐴)[cot⁑ 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴]γ€—)/([cot⁑ 𝐴 + 1 βˆ’ π‘π‘œπ‘ π‘’π‘ 𝐴]) = cot A + cosec A = R.H.S Hence proved

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

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.