Ex 8.3, 4 (iv) - Chapter 8 Class 10 Introduction to Trignometry

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Ex 8.3, 4 Prove the following identities, where the angles involved are acute angles for which the expressions are defined. ("1 + sec" A)/"sec A" ="sin2 A" /"1 โ€“ cos A" "[Hint : Simplify LHS and RHS separately]" (1 + secโก๐ด)/secโกใ€– ๐ดใ€— = 1/secโกใ€– ๐ดใ€— +secโกใ€– ๐ดใ€—/secโกใ€– ๐ดใ€— = 1/secโกใ€– ๐ดใ€— +1 = cos A + 1 (๐’”๐’Š๐’๐Ÿ ๐‘จ)/(1 โˆ’ cosโก๐ด ) = (๐Ÿ โˆ’ ๐’„๐’๐’”๐Ÿ ๐‘จ)/(1 โˆ’ cosโก๐ด ) = (12 โˆ’ ๐‘๐‘œ๐‘ 2 ๐ด)/(1 โˆ’ cosโก๐ด ) = ((1 โˆ’ ๐‘๐‘œ๐‘  ๐ด)(1+ cosโกใ€–๐ด)ใ€—)/(1 โˆ’ cosโก๐ด ) = 1 + cos A โˆด L.H.S = R.H.S Hence proved

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