Toolkit for Ex. 10.4 &Question No . 1

Lesson#2
Toolkit for Exercise 10.4
1) 2 sinα cosβ=sin⁡(α+β)+sin⁡(α−β)
2) 2 cosα sinβ=sin⁡(α+β)−sin⁡(α−β)
3) 2 cosα cosβ=cos⁡(α+β)+cos⁡(α−β)
4) −2 sinα sinβ=cos⁡(α+β)−cos⁡(α−β)
5) sinP+sinQ=2 sin⁡((P+Q)/2)cos((P−Q)/2)
6) sinP−sinQ=2 cos⁡((P+Q)/2)sin((P−Q)/2)
7) cosP+cosQ=2 cos⁡((P+Q)/2)cos((P−Q)/2)
8) cosP−cosQ=−2 sin⁡((P+Q)/2)sin((P−Q)/2)
And all the trigonometric knowledge of previous exercises . . .
Question No . 1
Q1:Express the following as sums or differences:
(i): 2sin3θ cosθ
(ii): 2cos5θ sinθ
(iii): sin5θ cos2θ
(iv): 2sin7θ sin2θ
(v): cos⁡(+)sin⁡(−)
(vi): cos⁡(2+30°)cos⁡(2−30°)
(vii): sin12° cos46°
(viii): sin⁡(+45°)sin⁡(−45°)
Q1:Express the following as sums or differences:
(iv): 2sin7θ sin2θ
(v): cos⁡(+)sin⁡(−)
(viii): sin⁡(+45°)sin⁡(−45°)
and Mathematics part 1 Example # 1(page #334).
Solve yourself . . . . .
Trigonometric Identities
Chapter No 10
Exercise No 10.4
Mathematics
part 1