Find the exact value of:
(1-sin^2 pi/2)/(cos^2 28 degrees + sin^2 28 degrees)
Come on.
the denominator is 1 (sin^2 ? + cos^2 ?)=1
the numberator is zero... sin PI/2=1
your teacher is pulling your leg.
not a joke. Just checking your knowledge of common identities and angles.
So, the exact value is 0/1 = 0.
To find the exact value of the given expression:
1. Start by simplifying the numerator and denominator separately.
- The numerator: (1 - sin^2(pi/2))
Since sin(pi/2) is equal to 1, we can substitute it into the expression.
1 - sin^2(pi/2) = 1 - 1^2 = 1 - 1 = 0
- The denominator: (cos^2(28 degrees) + sin^2(28 degrees))
According to the Pythagorean identity, sin^2(theta) + cos^2(theta) = 1.
Therefore, cos^2(28 degrees) + sin^2(28 degrees) = 1.
2. Substitute the simplified numerator and denominator back into the original expression.
0/1 = 0
Hence, the exact value of the given expression is 0.