Question

help please

a,b,c

b. 3.(12 pts.) Verify the following identities. a. cos(2x) = cos2x - sinºx sin2 x c. 2 sin? 1 + cos x sin(x + y) sin x cos y = 1- cotx tany

Answer 1

Now Taking {cco Cos(A+B) Cosacosb-sina sing =lt Cofnotany Solution @ We have to Verify that Cos(20) = Cos? - Sin²n L'HOS (Left hand side). Concan) = con(nan) = Conn.coon-sinn sinn = Cosno2_ (Sinny2 = cos²ri-sinin Thus Conan) = Cos?n-sin?n=R.H.S Hence proved 6 sinnty) -1-Cotntany Sinncosy Taking L.H.S Sinonty) SinnConytlosnsiny Sinn Cosy sinn Cony Cosmsing + sinm cosy Sinn. Cosy It Cosn Siny sinn cony = It cotnotany Thus Sin(nty) sinn cosy = Sinn Cany .

© 2 Sin? ( ) = sinn It coun Satu proof Since we know that & dividing by It conn to humerator &denominar Cosn= 1-2 sinan sinan > 2 simpanan - T-comm •Multiplyiny 3) 2 Sin?ma (i-connd* (ltro.com Itcoon of RoHS 3) 2 Sin? 6) ,² cos²n S:(9-b)(a+b)/ (1+Cosn) =a? 6?) I-cosen Itlosn Sin'ntcos?a=1 =) 2 Sin? () sinan sinin=lhosu 2 sin? (m/ Itlosn Hence 2 sin? (2) Sin²n It Cosn proved