1. Home
  2. >Year 12 Maths
  3. >Trigonometric Identities
Help

Sum and difference identities

All You Need in One Place

Everything you need for better marks in primary, GCSE, and A-level classes.

Learn with Confidence

We’ve mastered the UK’s national curriculum so you can study with confidence.

Instant and Unlimited Help

24/7 access to the best tips, walkthroughs, and practice questions.

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)
    Topic Notes
    ?
    Trig identities are formulas developed based on Pythagorean Theorem. These identities show us how and where to find the sine, cosine, and tangent of the sum and difference of two given angles.
    Download the Trigonometry identities chart here

    Formulas:
    sin⁡(A+B) \sin (A + B)
    sin⁡(A−B) \sin (A - B)
    cos⁡(A+B) \cos (A + B)
    cos⁡(A−B) \cos (A - B)
    tan⁡(A+B) \tan (A + B)
    tan⁡(A−B) \tan (A - B)
    Basic Concepts
    ?
    Related Concepts
    ?