Question No. 5

Lesson#7
Question No. 5
Q5: If α,β,γ are the angles of a triangle ABC, then prove that;
(i): sin⁡(α+β)=sin⁡γ|Solution:
Sum of three angles in a triangle is 180°|α+β+γ=180 ⇒α+β=180°−γ|sin⁡(α+β)=sin (180° −γ)|sin⁡(α+β)=sin γ (Proved)
Math.Ex.10.1, Part7(10.1),
(iii): cos⁡(α+β)=− sin⁡γ
(iv): tan⁡(α+β)+tan⁡γ" " =0
(ii): cos⁡((α+β)/2)=sin γ" " /2
This is the end of Ex. 10.1, now practice yourself.
Thanks.
Trigonometric Identities
Chapter No 10
Exercise No 10.1
Mathematics
part 1