# Discuss the continuity of the following functions (c)f(x)=sinx.cosx

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f(x) = sin(x).cos(x)

multiplying and diving by 2

f(x)= (1/2). 2sin(x).cos(x)

Using the identity 2sin(x).cos(x) = Sin(2x)

f(x) = (Sin 2x)/2

NOTE: AS TRIGNOMETRIC IDENTITIES ARE ALWAYS CONTINOUS, F(X) WOULD BE CONTINOUS TOO

hence F(x) is CONTINOUS at any value of x

multiplying and diving by 2

f(x)= (1/2). 2sin(x).cos(x)

Using the identity 2sin(x).cos(x) = Sin(2x)

f(x) = (Sin 2x)/2

NOTE: AS TRIGNOMETRIC IDENTITIES ARE ALWAYS CONTINOUS, F(X) WOULD BE CONTINOUS TOO

hence F(x) is CONTINOUS at any value of x

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