If x is the measure of an acute angle simplify the expressi

If x is the measure of an acute angle , simplify the expression

E=sin^2x*cos^2x*[1/square root[1-sin^2x*(1+cos^2x)]+1/square root[1-cos^2x*(1+sin^2x)]]

Solution

We have to simplify: E=sin^2x*cos^2x*[1/square root[1-sin^2x*(1+cos^2x)]+1/square root[1-cos^2x*(1+sin^2x)]]

=> sin^2x*cos^2x*[1/square root[1-(1-cos^2x)*(1+cos^2x)]+1/square root[1-(1-sin^2x)*(1+sin^2x)]]

=> sin^2x*cos^2x*[1/square root[1-(1-(cos^2x)^2)]+1/square root[1-(1-(sin^2x)^2]]

=> sin^2x*cos^2x*[1/square root[(cos^2x)^2)]+1/square root[(sin^2x)^2]]

=> sin^2x*cos^2x*[1/cos^2x +1/(sin^2x)]

=> sin^2x*cos^2x*[((sin^2x) + (cos^2x))/(cos^2x)*(sin^2x)]

=>1

The simplified expression is equal to 1.