Question

valueof sin(22.5°)×cos(22.5°)

Answer 1

sin. 45/2 = 1/root2 divided by 2 = 2/root 2
same cos 45/2 = 2/root 2
the answer is
2*2/2
2

Answer 2

The value of valueof sin(22.5°)×cos(22.5°) = 0.707106 (approximately )

Given problem:

Find the value of sin(22.5°)×cos(22.5°)

Solution:

Given sin(22.5°)×cos(22.5°)

As we know that from trigonometric ratios  

Sin 2A = 2 (SinA.CosA)

⇒ (SinA.CosA) =  (Sin 2A)/2

If Let A = 22.5°  ⇒ 2A = 2(22.5°) = 45°

⇒ sin(22.5°)×cos(22.5°)  = (Sin 45°)/2

Now calculate the value of (Sin 45°)/2

⇒ (Sin 45°)/2  = $\frac{\frac{1}{\sqrt{2} }}{2}$ = $\frac{1}{\sqrt{2} } (\frac{1}{2} )$  = $\frac{1}{\sqrt{2} (2)}$ = 0.707106 (approximately )

Therefore,

The value of valueof sin(22.5°)×cos(22.5°) = 0.707106 (approximately )

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