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# Trigonometric Functions of Sum and Difference of Two Angles

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#### description

• Identities Related to Sin 2x, Cos2x, Tan 2x, Sin3x, Cos3x and Tan3x.
• Deducing the Identities
• Deducing the identities like the following:-
tan(x+-y)=(tanx+-tany)/(1+-tanxtany)", "cot(x+-y)=(cotxcoty+-1)/(coty+-cotx)
sinalpha+-sinbeta=2"sin"1/2(alpha+-beta)"cos"1/2(alpha+-beta)
cosalpha+cosbeta=2"cos"1/2(alpha+beta)"cos"1/2(alpha-beta)
cosalpha-cosbeta=-2"sin"1/2(alpha+beta)"sin"1/2(alpha-beta)

#### notes

1) sin (-x)= -sin x

2)  cos (–x) = cos x

3) sin (x+y)= sin x cos y+ cos x sin y

4) sin (x-y)= sin x cos y- cos x sin y

5) cos (x+y)= cos x cos y- sin x sin y

6) cos (x-y)= cos x cos y+ sin x sin y

7) cos (π/2 - x)= sin x

8) cos (π/2 +x)= -sin x

9) cos (π- x)= -cos x

10) cos (π+ x)= -cos x

11) cos (2π- x)= cos x

12) sin (π/2 - x)= cos x

13) sin (π/2 + x)= cos x

14) sin (π- x)= sin x

15) sin (π+ x)= -sin x

16) sin (2π- x)= -sin x

17) tan (x+y)= (tan x+ tan y)/(1- tan x tan y)

18) tan (x-y)= (tan x- tan y)/(1+ tan x tan y)

19) cot (x+y)= (cot x cot y- 1)/(cot y+ cot x)

20) cot (x-y)= (cot x cot y+1)/cot y- cot x

21) sin2x= 2 sin x cos x

sin2x= (2 tan x)/(1+ tan^2x)

22) cos2x= cos^2 x- sin^2 x

cos2x= 2 cos^2 x- 1

cos2x= 1- 2 sin^2 x

cos2x= (1- tan^2 x)/(1+ tan^2 x)

23) tan2x= (2 tan x)/(1- tan^2 x)

24) sin3x= 3 sin x- 4 sin^3 x

25) cos3x= 4 cos^3 x- 3 cos x

26) tan3x= (3 tan x- tan^3 x)/(1- 3 tan^2 x)

27) cos x+ cos y= 2cos  (x+y)/2 cos  (x-y)/2

28) cos x- cos y= -2 sin  (x+y)/2 sin  (x-y)/2

29) sin x+ siny= 2 sin  (x+y)/2 cos  (x-y)/2

30) sin x- sin y= 2 cos  (x+y)/2 sin  (x-y)/2

31) sin (x+y)+ sin(x-y)= 2 sin x cos y

32) sin (x+y)- sin (x-y)= 2 cos x sin y

33) cos (x+y)+ cos (x-y)= 2 cos x cos y

34) cos (x+y)- cos (x-y)= 2 sin x sin y

35) 2 cos x cos y = cos (x + y) + cos (x – y)

36) –2 sin x sin y = cos (x + y) – cos (x – y)

37) 2 sin x cos y = sin (x + y) + sin (x – y)

38) 2 cos x sin y = sin (x + y) – sin (x – y)

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Trigonometric Ratios of Sum & difference of two angles [00:06:30]
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