Use a half-angle identity to find the exact solution

Ответ:

devoncruz23

13.01.2022

If , then $\cos x0$ .

Recall the double angle identity,

$\cos^2x=\dfrac{1+\cos(2x)}2$

so we have

$\cos^2\dfrac{3\pi}8=\dfrac{1+\cos\frac{6\pi}8}2=\dfrac{1-\frac1{\sqrt2}}2=\dfrac{2-\sqrt2}4$

$\implies\cos\dfrac{3\pi}8=\boxed{\dfrac{\sqrt{2-\sqrt2}}2}$

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ptrlvn01

29.03.2020

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property

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