Given that θ \theta\,θ satisfies the equation sin(2θ−45∘)=4cos(2θ−45∘)\sin(2\theta - 45^\circ) = 4 \cos(2\theta - 45^\circ)sin(2θ−45∘)=4cos(2θ−45∘).
Show that tan2θ=−53\displaystyle \tan 2\theta = -\frac{5}{3}tan2θ=−35
Hence find, in surd form, the exact value of tanθ\tan \thetatanθ, given that θ \theta\,θ is an obtuse angle.
348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.