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tation by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] sin(0) cos(0) Use this and composition of linear transformations to show the following trigonometric io cos(0, + 02) = cos(01) cos(02) – sin(61) sin(02) sin(61 + 02) = sin(81) cos(02) + cos(8,) sin(82) %3D

tation by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] sin(0) cos(0) Use this and composition of linear transformations to show the following trigonometric io cos(0, + 02) = cos(01) cos(02) – sin(61) sin(02) sin(61 + 02) = sin(81) cos(02) + cos(8,) sin(82) %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. In the lectures, we saw that the linear transformation of counter-clockwise rotation about the origin by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] [ sin(e) cos(e) cos(0) Use this and composition of linear transformations to show the following trigonometric identities: cos(01 + 02) = cos(04) cos(02) – sin(@1) sin(@2) %3D sin(0, + 02) = sin(01) cos(02) + cos(61) sin(@2)
Transcribed Image Text:8. In the lectures, we saw that the linear transformation of counter-clockwise rotation about the origin by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] [ sin(e) cos(e) cos(0) Use this and composition of linear transformations to show the following trigonometric identities: cos(01 + 02) = cos(04) cos(02) – sin(@1) sin(@2) %3D sin(0, + 02) = sin(01) cos(02) + cos(61) sin(@2)
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