Question

Under root sec square thrita + cosec square thrita = tan thrita + cot thrita plz plz its very urgent

Answer 1

Given, root sec^2 theta + cosec^2 theta

It can be written as,

          = root 1 + tan^2 theta + 1+ cot^2 theta

          = root 2 + tan^2 theta + cot^2 theta

          = root tan^2 theta + cot ^2 theta  + 2 tan theta cot theta

         = root (tan theta + cot theta)^2

         = tan theta + cot theta


Hope this helps!

Answer 2

Hi !

LHS = √sec²θ + cosec²θ
      

sec²θ = 1 + tan²θ         and     cosec²θ = 1 + cot²θ
          
         = √ 1 + tan²θ  + 1 + cot²θ
 
         = √  tan²θ  +  cot²θ + 2
       
        = √  tan²θ  +  cot²θ + 2 × 1

we know that ,
1 = tanθ × cot θ

hence ,


       = √  tan²θ  +  cot²θ + 2 ( tanθ × cot θ)


tan²θ  +  cot²θ + 2 ( tanθ × cot θ) is in the form of identity (a+b)² =a² + 2ab +b²
        
                     = √ (tan² +  cot²θ )²
  
                    = tanθ  +  cotθ 
               
                    = RHS