simplify 1 divided into bracket 1- sin 46 raise to power 2
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).
To simplify the expression 1 divided by (1 - sin^2 46), we need to first evaluate sin^2 46.
To find sin^2 46, we'll first find sin 46 and then square it.
Step 1: Find sin 46
To find sin 46, we can use a scientific calculator or reference table. The sine of 46 degrees is approximately 0.7193.
Step 2: Square sin 46
To square sin 46, multiply it by itself:
sin^2 46 = (0.7193) ^ 2 = 0.5178
Now, substitute the value of sin^2 46 into the expression:
1 / (1 - sin^2 46) = 1 / (1 - 0.5178)
To simplify further, subtract the value of sin^2 46 from 1:
1 - 0.5178 = 0.4822
Therefore, the simplified expression is:
1 / (1 - sin^2 46) = 1 / 0.4822.
To simplify the expression 1 divided by (1 - sin^2(46)), we can start by using the identity sin^2(x) + cos^2(x) = 1.
Since we have 1 - sin^2(46) in the denominator, we can rewrite it using the identity as:
1 - sin^2(46) = cos^2(46).
Now, our expression becomes 1 / (cos^2(46)).
To simplify this further, we can use the reciprocal identity for cos^2(x), which states that cos^2(x) = 1 / sec^2(x).
Applying this, we get:
1 / (cos^2(46)) = 1 / (1 / sec^2(46)).
The reciprocal of 1 / sec^2(46) is sec^2(46). So our simplified expression is:
1 / (1 / sec^2(46)) = sec^2(46).
Therefore, the simplified expression is sec^2(46).