ISC (Arts) Class 11CISCE
Share
Notifications

View all notifications

Trigonometric Functions of Sum and Difference of Two Angles

Login
Create free account


      Forgot password?

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)

Shaalaa.com | Trigonometric Ratios of Sum & difference of two angles

Shaalaa.com


Next video


Shaalaa.com


Trigonometric Ratios of Sum & difference of two angles [00:06:30]
S
Series 1: playing of 1
0%


S
View in app×