Question

Find the exact value without a calculator. \[ \cos 15^{\circ}=\frac{\sqrt{[?]+\sqrt{\square}}}{\square} \] Double-Angle Formulas: \( \sin (2 \theta)=2 \sin \theta \cos \theta \) \( \cos (2 \theta)=\cos ^{2} \theta-\sin ^{2} \theta \) \( \tan (2 \theta)=\frac{2 \tan \theta}{1-\tan ^{2} \theta} \) Half-Angle Formulas: \( \sin \left(\frac{\theta}{2}\right)= \pm \sqrt{\frac{1-\cos \theta}{2}} \) \( \cos \left(\frac{\theta}{2}\right)= \pm \sqrt{\frac{1+\cos \theta}{2}} \) \( \tan \left(\frac{\theta}{2}\right)= \pm \sqrt{\frac{1-\cos \theta}{1+\cos \theta}} \)

          Find the exact value without a calculator.
\[
\cos 15^{\circ}=\frac{\sqrt{[?]+\sqrt{\square}}}{\square}
\]

Double-Angle Formulas:
\( \sin (2 \theta)=2 \sin \theta \cos \theta \)
\( \cos (2 \theta)=\cos ^{2} \theta-\sin ^{2} \theta \)
\( \tan (2 \theta)=\frac{2 \tan \theta}{1-\tan ^{2} \theta} \)
Half-Angle Formulas: \( \sin \left(\frac{\theta}{2}\right)= \pm \sqrt{\frac{1-\cos \theta}{2}} \) \( \cos \left(\frac{\theta}{2}\right)= \pm \sqrt{\frac{1+\cos \theta}{2}} \) \( \tan \left(\frac{\theta}{2}\right)= \pm \sqrt{\frac{1-\cos \theta}{1+\cos \theta}} \)

Find the exact value without a calculator.

cos 15^∘=(√([?]+√(□)))/(□)

Double-Angle Formulas:
sin (2 θ)=2 sinθcosθ
cos (2 θ)=cos ^2θ-sin ^2θ
tan (2 θ)=(2 tanθ)/(1-tan ^2θ)
Half-Angle Formulas: sin((θ)/(2))= ±√((1-cosθ)/(2)) cos((θ)/(2))= ±√((1+cosθ)/(2)) tan((θ)/(2))= ±√((1-cosθ)/(1+cosθ))

Added by Amy B.

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