Example 17
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Example 17 Prove that sin〖5x − 〖2sin 3x +〗sinx 〗/𝑐𝑜𝑠〖5x − 𝑐𝑜𝑠x 〗 = tan x Taking L.H.S. sin〖5x + 〖sin x − 〗2sin3x 〗/𝑐𝑜𝑠〖5x − 𝑐𝑜𝑠x 〗 = 〖(sin〗〖5x + 〖sin x )− 〗2sin3x 〗/𝑐𝑜𝑠〖5x − 𝑐𝑜𝑠x 〗 Solving numerator and denominator separately Taking R.H.S sin〖5x + 〖sin x − 〗2sin3x 〗/𝑐𝑜𝑠〖5x −𝑐𝑜𝑠x 〗 Putting values = (2 sin3𝑥 cos2𝑥 −2 sin3𝑥)/(−2 sin〖3𝑥 sin2𝑥 〗 ) = (2 sin3𝑥 (cos〖2𝑥 − 1)〗)/(−2 sin〖3𝑥 sin2𝑥 〗 ) = ( (cos〖2𝑥 −1)〗)/(−sin2𝑥 ) = ( −(cos〖2𝑥 −1) 〗)/sin2𝑥 = (〖1 − cos〗2𝑥 )/sin2𝑥 = (1 − (1 − 2 sin2𝑥 ) )/(2 cos〖𝑥 〗 sin𝑥 ) = (0 + 2 sin2𝑥)/(2 cos〖𝑥 〗 sin𝑥 ) = (2 sin2𝑥)/(2 cos〖𝑥 〗 sin𝑥 ) = sin〖𝑥 〗/cos〖𝑥 〗 = tan x = R.H.S. Hence L.H.S. = R.H.S. Hence proved
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17 You are here
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24 Important
Example 25
Example 26
Example 27 Important
Example 28 Important
Example 29
Chapter 3 Class 11 Trigonometric Functions
Serial order wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.