Question

2cos^2 (45-a/2)/cos a

Answer 1

Применена формула половинного угла косинуса

Answer 2

To simplify the expression 2cos^2(45 - a/2) / cos(a), we can use trigonometric identities. Let's break it down step by step:

Step 1: Simplify the numerator We have 2cos^2(45 - a/2). Using the double-angle identity for cosine, we can rewrite it as: 2cos^2(45 - a/2) = 2[cos^2(45)cos^2(-a/2) - sin^2(45)sin^2(-a/2)] = 2[(√2/2)^2cos^2(-a/2) - (√2/2)^2sin^2(-a/2)] = 2[1/2cos^2(-a/2) - 1/2sin^2(-a/2)] = cos^2(-a/2) - sin^2(-a/2) = cos^2(-a/2) - (1 - cos^2(-a/2)) [Using the identity sin^2θ = 1 - cos^2θ] = 2cos^2(-a/2) - 1

Step 2: Simplify the denominator We have cos(a).

Now, substituting the simplified numerator and denominator back into the original expression, we have:

(2cos^2(45 - a/2)) / cos(a) = (2cos^2(-a/2) - 1) / cos(a)

Please note that this is the simplified form of the expression. If you have a specific value for 'a', you can further evaluate it numerically.