1. Home
  2. >GCE N(A)-Level A Maths
  3. >Trigonometric Identities
Help

Sum and difference identities

0/8
?
Examples
Lessons
  1. Simplify expressions
    1. sin 24°cos 36° + cos 24°sin 36°
    2. tan2π5−tan3π201+tan⁡2π5⋅tan⁡3π20\frac{tan {2 \pi \over 5 } - tan {3 \pi \over 20}}{1 + \tan {2 \pi \over 5} \cdot \tan {3 \pi \over 20}}
  2. Prove Identities
    1. sin⁡(A−B)sin⁡B+cos⁡(A−B)cos⁡B=sin⁡Asin⁡Bcos⁡B \frac{\sin (A - B)}{\sin B} + \frac{\cos (A - B)}{\cos B} = \frac{\sin A}{\sin B \cos B}
    2. 1+tan⁡Atan⁡(A+π4)=1−tan⁡A\frac{1 + \tan A}{\tan (A + {\pi \over 4})} = 1 - \tan A
  3. Without using a calculator, evaluate:
    1. sin 15°
    2. sec (-105°)
    3. tan 19π12{19\pi \over 12}
  4. Given sin⁡A=−45\sin A = -{4 \over5} and cos⁡B=1213\cos B = {12 \over 13},
    where π≤A≤3π2\pi \leq A \leq {3 \pi \over 2} and 3π2≤B≤2π{3 \pi \over 2} \leq B \leq 2\pi,
    find the exact value of cos⁡(A+B)\cos (A + B)