Ex 8.3

Chapter 8 Class 10 Introduction to Trignometry
Serial order wise

### Transcript

Ex 8.3, 4 Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ii) "cos A" /"1 + sin A" +"1 + sin A" /"cos A" =2 sec A Taking L.H.S (cosβ‘ π΄)/(1 + sinβ‘γ π΄γ )+(1 + sinβ‘ π΄)/(cosβ‘ π΄) = (cosβ‘ π΄ (cosβ‘ π΄) + (1 + sinβ‘ π΄)(1 + sinβ‘γ π΄)γ)/((1 + sinβ‘ π΄)(cosβ‘ π΄)) = (πππππ¨ + (π + π¬π’π§β‘π¨ )π)/((π + πππβ‘ π¨)(πππβ‘π¨)) = (πππ 2 π΄ + 1^2 + π ππ2 π΄ + 2 sinβ‘π΄)/((1 + sinβ‘ π΄)(cosβ‘π΄)) = ((ππππ π¨ + ππππ π¨) + 1 + 2 sinβ‘ π΄)/((1 + sinβ‘γ π΄)(cosβ‘ π΄)γ ) As cos2 A + sin2 A = 1 = (π + 1 + 2 sinβ‘π΄)/((1 + sinβ‘γ π΄)(cosβ‘ π΄)γ ) = (2 + 2 sinβ‘ π΄)/((1 + sinβ‘γ π΄)(cosβ‘ π΄)γ ) = (2(1+ sinβ‘ π΄))/((1 + sinβ‘γ π΄)(cosβ‘ π΄)γ ) = π/(πππβ‘ π¨) = 2 Γ1/cosβ‘γ π΄γ = 2 sec A = R.H.S β΄ L.H.S = R.H.S Hence proved