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T3 - Ts – Tg – Ty+ cos" e, prove that -62. If Th = sin"1

Answer»

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{(sinx^3+ cosx^3)-(sinx^5+ cosx^5)}/sinxcosx={ sinx^3+ cosx^3- sinx^5-cosx^5}/sinxcosx={sinx^3(1-sinx^2)+cosx^3(1-cosx^5)}/sinxcosx={ sinx^2cosx^2(sinx+cosx)}/sinx+ cosx= sinx^2cosx^2; RHS: {(sinx^5+ cosx^5)-( sinx^7+ cosx^7)}/sinx^3+ cosx^3= { sinx^5-sinx^7+ cosx^5- cosx^7}/ sinx^3+cosx^3 ={sinx^5(1- sinx^2)+ cosx^5(1- cosx^5)}/sinx^3+ cosx^3={ sinx^5( cosx^2)+ cisx^5( sinx^2)}/sinx^3+ cosx^3={sinx^2cosx^2{ sinx^3+ cosx^3}/sinx^3+ cosx^3=sinx^2cosx^2; since RHS= LHS

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