The greatest value of sin x cos x is
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The greatest value of sin x cos x is
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Answer:
let fx=sinx.cosx=2sinx.cosx/2=(sin2x.)/2
derivative. both side
f'x=1/2×2.cos2x
for max or min value.
f'x=0
cos2x=0
2x=90°
x=45°
second derivative both side
f"x=-2sin2x.
let x=45°
f"x=-2(-ve)
f"x is negative , so value is greatest.
let x= 45° ,in fx
fx= sin45°.cos 45°=1/√2×1/√2=1/2
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