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If sec A + tan A = p, then the value of sin A is?

If sec A + tan A = p, then the value of sin A is?

Grade:12th Pass

1 Answers

vikas askiitian expert
509 Points
11 years ago

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 eq and roots of eq are


sinA = [-b+(-)(b2-4ac)1/2]/2a

       =-1 ,  (p2-1/p2+1)

sinA = -1 cannot be the root of the eq because it doesnot satisfies the given eqpression so

the only root is

sinA = p2-1/p2+1

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