HPC 1.4-1.5 practice 1

[math]\sin2x[/math]

[math]\cos2x[/math]

[math]\csc2x[/math]

[math]\sec2x[/math]

[math]\dfrac{1}{2}[/math]

[math]\dfrac{1}{\sqrt{2}}[/math]

[math]1-\dfrac{1}{\sqrt{2}}[/math]

[math]1-\dfrac{2}{\sqrt{2}}[/math]

[math]\theta[/math] is unique

[math]\theta[/math] is in the interval [math][\pi, 2\pi][/math]

[math]\tan\theta=\dfrac{1}{\sqrt{8}}[/math]

[math]\theta[/math] is a solution to the equation [math]3\sin\theta-1=0[/math]

[math]\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right][/math]

[math]\left[-\dfrac{\pi}{3},\dfrac{\pi}{3}\right][/math]

[math]\left[-\dfrac{\pi}{4},\dfrac{\pi}{4}\right][/math]

[math]\left[-\dfrac{\pi}{6},\dfrac{\pi}{6}\right][/math]

[math]\sqrt{24}[/math]

[math]-\sqrt{24}[/math]

[math]\dfrac{1}{\sqrt{24}}[/math]

[math]-\dfrac{1}{\sqrt{24}}[/math]

[math]2\sin20^\circ \cos20^\circ[/math]

[math]\cos^220^\circ+\sin^220^\circ[/math]

[math]2\sin^220^\circ-1[/math]

[math]\cos^220^\circ-\sin^220^\circ[/math]

[math]\cos^{-1}(\cos(-1))=-1[/math]

[math]\cos(\cos^{-1}(-1))=-1[/math]

[math]\tan^{-1}(\tan(-1))=-1[/math]

[math]\tan^{-1}(\tan^{-1}(-1))=-1[/math]

[math]\dfrac{x^2+y^2}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]

[math]\dfrac{1+xy}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]

[math]\dfrac{x^2-y^2}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]

[math]\dfrac{1-xy}{\sqrt{1+x^2}\sqrt{1+y^2}}[/math]