Question

Find the
range of
the function
ecosx-l​

Answer 1

Answer:

$=f(x)=tan(sinx+cosx)</p><p>y=tan[2sin(x+4π)]</p><p>The above step has come by using the expansion of sin(x+4π)=sin4πcosx+cos4πsinx=2(sinx+cosx)</p><p>Clearly, f(x) is defined for all real values of x as domain of sine function is R.</p><p></p><p>Range :</p><p>−1≤sin(x+4π)≤1</p><p>⇒−2≤2sin(x+4π)≤2</p><p>⇒−tan2tan[2sin(x+4π)]≤tan2</p><p>⇒−tan2≤y≤tan2</p><p></p><p></p><p>Range of f is [−tan2,tan2]</p><p></p><p>$

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