Ex 8.3

Chapter 8 Class 10 Introduction to Trignometry
Serial order wise

### Transcript

Prove the following identities, where the angles involved are acute angles for which the expressions are defined. ((1 +π‘ππ2 π΄)/(1 + πππ‘2 π΄))=((1 βtanβ‘γ π΄γ)/(1 βcotβ‘ π΄))^2=π‘ππ2 π΄ Solving ((π + ππππ π¨)/(π + ππππ π¨)) ((1 + π‘ππ2 π΄)/(1 + ππππ π΄)) = ((1 + π‘ππ2 π΄))/(((1+ π/(ππππ π¨)) ) = ((1 + π‘ππ2 π΄))/(((tan^2β‘π΄ + 1))/(tan^2β‘π΄ ))= (π‘ππ2 π΄ (1 + π‘ππ2 π΄))/((π‘ππ2 π΄ + 1)) = tan2 A = R.H.S Solving ((πβ πππβ‘π¨)/(πβ πππβ‘π¨ ))^π ((1β tanβ‘π΄)/(1β πππβ‘π¨ ))^2 = ((1 β tanβ‘γ π΄γ)/(1 β π/πππβ‘γ π¨γ ) " " )^2 = (((1 β tanβ‘γ π΄)γ)/(((tanβ‘γ π΄ β1γ ))/tanβ‘γ π΄γ ))^2 = (tanβ‘γ π΄(1 β tanβ‘γ π΄)γ γ/( (tanβ‘γ π΄ β1)γ ))^2 = (tanβ‘γ π΄(1 β tanβ‘γ π΄)γ γ/(β(1 β tanβ‘γ π΄)γ ))^2 = (βtanβ‘π΄ )^2 = tan2 A = RHS Therefore, ((1 + π‘ππ2 π΄)/(1 + πππ‘2 π΄))=((1 β tanβ‘γ π΄γ)/(1 β cotβ‘ π΄))^2=π‘ππ2 π΄ H\ence proved

#### 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.