This document contains instructions for a trigonometry and differentiation assignment with the following problems: 1) Solve an equation involving sin for theta. 2) Simplify trigonometric expressions involving sin, cos, and tan. 3) Find the value of tan(A + B) given tan A and tan B. 4) Show that an expression involving a trigonometric function is equal to another expression. 5) Prove trigonometric identities involving sin, cos, and tan. 6) Differentiate several functions with respect to x. There are also two extension problems: solving an equation involving sin and cos, and proving and applying an identity involving tan.

1. C3 Trigonometry 2 and Differentiation 1 Assignment<br />DUE: Tuesday 14th December<br />1)Solve the equation sin = 2sin (600 –) for . [4]<br />2)Simplify the following:<br />(a)[2]<br />(b)cos 40° cos 20° – sin 40°sin 20°[2]<br />3) If tan A = and tan B = , find the value of tan (A + B) without a calculator.[2]<br />4) If , show that .[3]<br />5) Prove the following identities:<br />(a)tan( + 45°) + tan( - 45°) 2tan2[4]<br />(b)(sin A + cos A)(sin 2A – cos 2A) <br /> sin A – cos 3A[4]<br />6)Differentiate the following functions with respect to x:<br />(a)(b)<br />(c)(d)(e)(f)(g)(h)[16] <br />Total: 37 <br />EXTENSION:<br />1. Solve the following equation, for 0 x , giving your answers in terms of .<br />sin 5x – cos 5x = cos x – sin x.<br />[8]<br />2. Prove that <br />tan14π-12x≡secx-tanx (*)<br />(i) Use (*) to find the value of tan18π. Hence show that <br />tan1124π=3+2-13-6+1<br />(ii) Show that <br />3+2-13-6+1=2+2+3+6<br />(iii) Use (*) to show that <br />tan148π=16+102+83+66-2-2-3-6<br />[20]<br />