Ex 8.4, 5 (vi) - Chapter 8 Class 10 Introduction to Trignometry (Term 1)

Transcript

Ex 8.4, 5 Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (vi) ((1 + sin )/(1 sin )) = sec A + tan A Taking L.H.S ((1 + sin )/(1 sin )) Rationalizing denominator Multiplying (1 + sin A) in numerator and denominator = (((1 + sin )(1 + sin ) )/((1 sin )(1 + sin ) )) = (((1 + sin )2 )/(12 2 )) = (((1 + sin )2 )/(1 2 )) = (((1 +sin )2 )/( 2 )) = (((1 + )/( ))^2 ) = (1 + sin )/cos = 1/cos + sin /cos = sec A + tan A = R.H.S Hence proved