If secA+tanA=p prove that sinA=(p^2-1)/(p^2+1)

 

 

 

 

 

 

 

 

 

 

Hello student,
please find the answer to your question below
secA+tanA =p
1+sinA/cosA =p
1+sinA = pcosA
squaring both sides
1+ sin²A + 2sinA = p²cos²A (cos²A = 1-sin²A)
sin²A(1+p²) + 2sinA + 1-p² = 0
this is a quadratic equation and roots of equation are
sinA = [-b+(-)(b2-4ac)^1/2]/2a
=-1,(p²-1/p²+1)
sinA = -1 cannot be the root of the equation because it doesnot satisfies the given eqpression sothe only root is
sinA = p²-1/p²+1