DP Mathematics HL Questionbank

• Syllabus

3.3

Sub sections and their related questions

Compound angle identities.

• 12M.1.hl.TZ1.5b: Simplify the expression \(\frac{{\sin 3x}}{{\sin x}} - \frac{{\cos 3x}}{{\cos x}}\).
• 12M.1.hl.TZ2.9: Show that \(\frac{{\cos A + \sin A}}{{\cos A - \sin A}} = \sec 2A + \tan 2A\) .
• 12N.1.hl.TZ0.8b: Hence, show that \(\tan \theta  = \frac{1}{{1 + 2\pi }}\), where \(\theta \) is the acute angle...
• 08M.1.hl.TZ2.3: In the diagram below, AD is perpendicular to BC. CD  =  4, BD  =  2 and AD  =  3....
• 13M.1.hl.TZ1.12f: Prove that \(\int_1^{3.5} {\frac{1}{{4{x^2} - 4x + 5}}{\text{d}}x = \frac{\pi }{{16}}} \).
• 10M.1.hl.TZ1.13: (a)     Show that...
• 10M.1.hl.TZ2.6: If x satisfies the equation...
• 13M.1.hl.TZ2.10a: Given that...
• 13M.1.hl.TZ2.10b: Hence find the value of...
• 11N.2.hl.TZ0.4a: Given that...
• 11M.1.hl.TZ1.5a: Show that \(\frac{{\sin 2\theta }}{{1 + \cos 2\theta }} = \tan \theta \) .
• 11M.1.hl.TZ1.5b: Hence find the value of \(\cot \frac{\pi }{8}\) in the form \(a + b\sqrt 2 \) , where...
• 13N.1.hl.TZ0.8: (a)     Prove the trigonometric identity \(\sin (x + y)\sin (x - y) = {\sin ^2}x - {\sin...
• 14N.1.hl.TZ0.13b: (i)     Use the double angle identity...
• 14N.2.hl.TZ0.14a: Show that \(\sin (B + C) = \frac{1}{2}\).
• 15N.1.hl.TZ0.8a: Show that \(\sin \left( {\theta  + \frac{\pi }{2}} \right) = \cos \theta \).
• 16M.1.hl.TZ1.5b: By writing \(15^\circ \) as \(60^\circ  - 45^\circ \) find the value of \(\cos (15^\circ )\).
• 18M.2.hl.TZ1.3: Let ...

Double angle identities.

• 12M.1.hl.TZ2.2: Find the values of x for which the vectors...
• 12M.1.hl.TZ2.9: Show that \(\frac{{\cos A + \sin A}}{{\cos A - \sin A}} = \sec 2A + \tan 2A\) .
• 12N.1.hl.TZ0.1: Given that \(\frac{\pi }{2} < \alpha  < \pi \) and \(\cos \alpha  = - \frac{3}{4}\), find...
• SPNone.1.hl.TZ0.1b: Find the value of \(\tan 2\theta \) .
• SPNone.1.hl.TZ0.1c: Find the value of \(\cos \left( {\frac{\theta }{2}} \right)\) , giving your answer in the form...
• 11N.1.hl.TZ0.4b: show that \({\left( {f(x)} \right)^2} = \frac{3}{2} + 2\sin x - \frac{1}{2}\cos 2x\);
• 12M.1.hl.TZ1.10b: By squaring both sides of the equation in part (a), solve the equation to find the angles in the...
• 14M.1.hl.TZ1.5b: Find a similar expression for \(\sin \frac{1}{2}x,{\text{ }}0 \leqslant x \leqslant \pi \).
• 14M.1.hl.TZ1.10: Given that \(\sin x + \cos x = \frac{2}{3}\), find \(\cos 4x\).
• 14M.1.hl.TZ2.9: The first three terms of a geometric sequence are \(\sin x,{\text{ }}\sin 2x\) and...
• 14M.1.hl.TZ1.5a: Use the identity \(\cos 2\theta  = 2{\cos ^2}\theta  - 1\) to prove that...
• 14N.1.hl.TZ0.13b: (i)     Use the double angle identity...
• 15N.1.hl.TZ0.9: Solve the equation \(\sin 2x - \cos 2x = 1 + \sin x - \cos x\) for...
• 16M.1.hl.TZ1.5b: By writing \(15^\circ \) as \(60^\circ  - 45^\circ \) find the value of \(\cos (15^\circ )\).
• 16N.1.hl.TZ0.13b: Show that \(\frac{{1 - \cos 2x}}{{2\sin x}} \equiv \sin x,{\text{ }}x \ne k\pi \) where...
• 18M.2.hl.TZ1.3: Let ...