Dr. J's Maths.com
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Trigonometry - Further trigonometric identities - angle sum and difference.
Test Yourself 1.


 

The results required for these further identities are:

sin (A ± B) = sin A cos B ± cos A sin B

cos (A + B) = cos A cos B - sinA sin B

Expanding terms. Expand sin (2x + y). Expand cos (2x - y).
  Expand tan (4α - 3β). Expand and simplify
tan (A + 45°).
  Find the exact value of sin (75°) by expanding sin (30° + 45°) and simplifying with exact values. Find the exact value of
cos (105°) by expanding cos (60° + 45°) and simplifying with exact values.
     
  Expand sin ((a+b) - c). Expand cos ((3α + 2β)+ γ).
  Expand cos (2θ + 60°). Expand tan (x + 135°).
     
Simplifying. cos 60°cos 30° - sin 60° sin 30°. sin 60°cos 30° - cos 60° sin 30°.
     
     
 

Simplify

sin (2α + β) cosβ - cos (2α + β)sin (β)

  
     
     
Evaluating.

If ,

where 0 < β < α < 90°, evaluate

(i) sin (α - β).

(ii) tan (α + β).

(iii) cos (α - β).

  
Equations.

(i) Show that

(ii) Hence find the solutions for

tan 2x + tanx = 0 in the domain [0, 90°].