if f(x)=left parenthesis sin x minus cos x right parenthesis squared the maximum value of f(x) is ?

Asked by araima2001 | 8th Nov, 2015, 06:51: AM

Expert Answer:

begin mathsize 11px style open parentheses sinx space minus space cosx close parentheses squared equals stack sin squared straight x plus cos squared straight x with underbrace below space minus space stack 2 sinxcosx with underbrace below equals space space space space space space space space space 1 space space space space space space space space space space minus space space space sin 2 straight x equals 1 minus sin 2 straight x To space maximize space the space above comma space we space have space to space minimize space sin 2 straight x. The space minimum space value space of space sin 2 straight x space is space minus 1. Hence comma space maximum space value space of space 1 space minus space sin space 2 straight x space is space 1 minus open parentheses negative 1 close parentheses equals 2. So space the space maximum space value space of space open parentheses sinx space minus space cosx close parentheses squared space is space 2. end style

Answered by satyajit samal | 8th Nov, 2015, 08:35: AM

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