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
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Example 17 You are here
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About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.