Given that θ \theta\,θ satisfies the equation sin(2θ−45)=3cos(2θ−45)\sin(2\theta - 45) = 3 \cos(2\theta - 45)sin(2θ−45)=3cos(2θ−45).
Show that tan2θ=−2\tan 2\theta = -2tan2θ=−2
Show that tan2θ−tanθ−1=0\tan^2\theta - \tan\theta - 1 = 0tan2θ−tanθ−1=0
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.