Question

cos1° - cos 89° = sin 89° - sin 1°​

Answer 1

LHS

LHScos 1 - cos 89

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHS

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)=2 sin (44) cos (45)

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)=2 sin (44) cos (45)= 2 sin (44) (1/√2)

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)=2 sin (44) cos (45)= 2 sin (44) (1/√2)=√2 sin 44

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)=2 sin (44) cos (45)= 2 sin (44) (1/√2)=√2 sin 44 LHS=RHS

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)=2 sin (44) cos (45)= 2 sin (44) (1/√2)=√2 sin 44 LHS=RHS Hence Proved

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)=2 sin (44) cos (45)= 2 sin (44) (1/√2)=√2 sin 44 LHS=RHS Hence ProvedI hope you get it!

LHScos 1 - cos 89= -2 sin(1+89/2) sin(1-89/2)= -2 sin 45 sin (-44). sin(-a)=- sin (a)= 2 (1/√2) sin 44=√2 sin 44RHSsin 89-sin 1=2 sin (89-1/2) cos(89+1/2)=2 sin (44) cos (45)= 2 sin (44) (1/√2)=√2 sin 44 LHS=RHS Hence ProvedI hope you get it!Please mark Brainliest if you like it!!

Answer 2

Answer:

$\huge \underline{ \red { \bf{Question}}}$

${ \tt{cos1° - cos89° = sin89° - sin1°}}$

Solution:-

${ \implies{ \tt{cos1 - cos89 = sin89 - sin1}}}$

${ \implies{ \tt{cos(90 - 89) - cos(90 - 1) = sin89 - sin1}}}$

${ \implies{ \tt{sin89 - sin1 = sin89 - sin1}}}$

Hence proved ✔