Show that the equation
2sec2x+4tan2x+10secx=02\sec^2 x + 4\tan^2 x + 10\sec x = 02sec2x+4tan2x+10secx=0
can be written in the form
asec2x+bsecx+c=0a\sec^2 x + b\sec x + c = 0asec2x+bsecx+c=0
where aaa, b b\,b and c c\,c are integers with a>0 a > 0\,a>0 and with no common factor other than 1.
Hence, given that x x\,x is obtuse, find the exact value of tanx\tan xtanx.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.