Given cos(75∘)=6−24\displaystyle \cos(75^\circ) = \frac{\sqrt{6} - \sqrt{2}}{4}cos(75∘)=46−2 and sin(75∘)=6+24\displaystyle \sin(75^\circ) = \frac{\sqrt{6} + \sqrt{2}}{4}sin(75∘)=46+2. Show that tan2(75∘)\tan^2(75^\circ)tan2(75∘) can be written in the form a+b3a + b\sqrt{3}a+b3. Fully justify your answer.
41 exam-style questions on Edexcel A Level Maths Trigonometric Identities and Equations, covering 10.1 Angles in all four Quadrants, 10.2 Exact Values of Trigonometric Ratios, 10.3 Trigonometric Identities, 10.4 Solving Trigonometric Equations, 10.5 Harder Trigonometric Equations, and 10.6 Equations and Identities. Each one has a worked solution and a mark scheme showing where the marks go.