Question

show geometrically cos 45 degree

Answer 1

HEY MATE HERE IS YOUR ANSWER--

Q) COS 45 DEGREE GEOMETRICALLY?
ANS.

Geometrically find the value of cos45 DEGREE

Let ΔABC be a right angle Δ with ∠B = 90° and ∠BAC = 45°

∴∠ACB will also be 45°

∵∠BAC = ∠ACB = 45°

∴ AB = BC

Let AB = x

Then BC = x (∵AB = BC)

By Pythagorean Theorem,

AC = √(AB² + BC²)

      = √(x² + x²)  (∵ AB = BC = x)

      =√(2x²)

∴ AC = √2 x

Now we know that cosФ = base/hypotenuse

∴ cos∠BAC = AB/AC

or, cos45° = x/√2 x  (∵ ∠BAC = 45°)

∴ cos45° = 1/√2

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