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

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

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
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

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