Given that y=tanxy = \tan xy=tanx, use the quotient rule to show that dydx=sec2x\frac{dy}{dx} = \sec^2 xdxdy=sec2x
The cross-section of a high-precision optical lens is modeled by the region bounded by the curve y=3tan2x+2y = 3\tan^2 x + 2y=3tan2x+2, the xxx-axis, and the vertical boundaries x=π6x = \frac{\pi}{6}x=6π and x=π3x = \frac{\pi}{3}x=3π.
Show that the area of this cross-section is 33−3−π63\sqrt{3} - \sqrt{3} - \frac{\pi}{6}33−3−6π
which simplifies to 23−π62\sqrt{3} - \frac{\pi}{6}23−6π
Fully justify your answer.
Practise Edexcel A Level Maths 11.3 Using Trigonometric Identities with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.