CBSE Class 11-science Answered
Prove that
Sin5A= 5Cos^5 A. SinA -10cos^2 A. Sin^3 A+ Sin^5 A
Asked by aakashpachisia1488 | 07 Aug, 2011, 06:15: PM
Expert Answer
By de moivres:
cos5A + i sin5A = (cosA + i sinA)5
Expanding, we get:
cos5a + i sin5a = cos5a + 5 cos4a i sina + 10 cos3a i2 sin2a + 10 cos2a i3 sin3a + 5 cosa i4 sin4a + i5 sin5a
Using i2=-1, i3= -i, i4=1, i5=i, we get
cos5a + i sin5a = cos5a + 5 cos4a i sina - 10 cos3a sin2a - 10 cos2a i sin3a + 5 cosa sin4a + i sin5a
Equating imaginary parts,
sin5a = 5 cos4a sina - 10 cos2a sin3a + sin5a
Answered by | 09 Aug, 2011, 03:33: AM
Concept Videos
-
Trigonometric identities and problems
Fundamental trigonometric identities and problems based on them. Sign Conve... -
Degree measure and Radian measure ...
This video explains the concept of negative & positive angles, conversion o... -
Domain, period and range of trigonometric functions ...
Define the domain, period and range of the trigonometric functions and plot... -
Basic Trigonometric Formulae
Derive and apply the basic formulae of sine and cosine functions like sin(... -
Sign of Trigonometric Functions
This video covers values of trigonometric ratios of angles greater than 90 ...
CBSE 11-science - Maths
Asked by rajyothi64 | 05 Mar, 2024, 09:49: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by ghoshshawata62 | 04 Mar, 2024, 08:16: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by nayaktapaswini2007 | 29 Feb, 2024, 09:10: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by bimanmandal53361 | 15 Jan, 2024, 12:32: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by sreyas.katuri | 23 Sep, 2023, 07:12: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by 069.pks | 16 Sep, 2023, 10:06: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by surekhashriwas01 | 12 Sep, 2023, 08:39: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by mvr23467 | 12 Sep, 2023, 07:52: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by SasipriyaNagappan | 27 Jul, 2023, 07:22: PM
ANSWERED BY EXPERT
