Math, asked by Anonymous, 1 year ago

Help me guys......

Prove that :-tanA/(1-cotA) + cotA/(1-tanA) = secA*cosecA+1.

Answers

Answered by kunal0912
1
LHS = tanA/1-cotA + cotA/1-tanA
 
        = sinA/cosA/1-cosA/sinA + cosA/sinA/1-sinA/cosA
       
        = sinA/cosA/sinA-cosA/sinA + cosA/sinA/cosA-sinA/cosA
      
        = sin²A/cosA(sinA-cosA) + cos²A/(cosA-sinA)sinA
    
        = sin²A/cosA(sinA-cosA) - cos²A/(sinA-cosA)
         
        = sin³A-cos³A/(sinA-cosA)(sinAcosA)
        = (sinA-cosA)(sin²A+cos²A + sinAcosA)/(sinA-cosA)(sinAcosA)                                                                               [By using a³-b³ = (a-b)                                                                                                   (a²+ab+b²)]

    

        = 1+sinAcosA/sinAcosA
   
        = 1/sinAcosA + sinAcosA/sinAcosA
        = secA*cosecA + 1 = RHS  

  
 

Anonymous: Thanks dear friend
kunal0912: friend ko thanks ni bolte hehe
Anonymous: Ok.......
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