Question 5 (ii) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ii) cosA(1+sinA)+(1+sinA)cosA=2secA
Open in App
Solution
(ii) cosA(1+sinA)+(1+sinA)cosA=2secA L.H.S.=cosA(1+sinA)+(1+sinA)cosA=[cos2A+(1+sinA)2](1+sinA)cosA=(cos2A+sin2A+1+2sinA)(1+sinA)cosA=(1+1+2sinA)(1+sinA)cosA=(2+2sinA)(1+sinA)cosA=2(1+sinA)(1+sinA)cosA=2cosA=2secA=R.H.S.