Evaluating using Trignometric Identities

Chapter 8 Class 10 Introduction to Trignometry
Concept wise

Transcript

Example 11 Prove that cotβ‘γπ΄ β cosβ‘π΄ γ/cotβ‘γπ΄ + cosβ‘π΄ γ =(πππ ππ π΄ β 1)/(πππ ππ π΄ + 1) Taking L.H.S cotβ‘γπ΄ βγ cosγβ‘π΄ γ/cotβ‘γπ΄ +γ cosγβ‘π΄ γ Writing everything in terms of sin A and cos A = (cosβ‘γ π΄γ/sinβ‘γ π΄γ βγ cosγβ‘γ π΄γ)/(cosβ‘γ π΄γ/sinβ‘γ π΄γ +γ cosγβ‘γ π΄γ ) = cosβ‘γ π΄ βγ cosγβ‘γ π΄ sinβ‘γ π΄γ γ γ/(sinβ‘γ π΄γ/(cosβ‘γ π΄ + cosβ‘γ π΄ sinβ‘γ π΄γ γ γ/sinβ‘γ π΄γ )) = ( (πππβ‘γ π¨γ β πππβ‘γ π¨γ sinβ‘γ π΄ γ))/((πππβ‘γ π¨γ + πππβ‘γ π¨γ sinβ‘γ π΄ γ)) = (πππβ‘γ π¨γ (1 β sinβ‘γ π΄ γ))/(πππβ‘γ π¨γ (1 + sinβ‘γ π΄ γ)) = ( (1 β sinβ‘γ π΄ γ))/( (1 + sinβ‘γ π΄ γ)) Dividing sin A on numerator and denominator = ( ((1 β sinβ‘γ π΄ γ))/(πππ π¨))/( ((1 + sinβ‘γ π΄ γ))/(πππ π¨ )) = ( 1/(π ππ π΄) β (π ππ π΄)/(π ππ π΄))/(1/(π ππ π΄) + (π ππ π΄)/(π ππ π΄)) = ( 1/(π ππ π΄) β 1)/(1/(π ππ π΄) + 1) = (πππππ π¨ β π)/(πππππ π¨ + π) = R.H.S. So, L.H.S = R.H.S Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.