simplify 1 divided into bracket 1- sin 46 raise to power 2

Answer 1

To simplify the expression 1 / (1 - sin^2(46)), we first note that the equation sin^2(x) + cos^2(x) = 1 holds true for any angle x.

Therefore, we can rewrite the expression as follows:

1 / (1 - sin^2(46)) = 1 / cos^2(46)

Next, we can use the identity cos^2(x) = 1 - sin^2(x) to substitute for cos^2(46):

1 / cos^2(46) = 1 / (1 - sin^2(46))

Substituting back into the original expression, we get:

1 / (1 - sin^2(46)) = 1 / (1 - (1 - cos^2(46)))

Simplifying further:

1 / (1 - sin^2(46)) = 1 / (1 - 1 + cos^2(46))

1 / (1 - sin^2(46)) = 1 / cos^2(46) (since 1 - 1 cancels out)

Therefore, the simplified expression is 1 / cos^2(46).