Question

. If secA+ tanA=P then express the value of SinA in terms of ‘P’.​

Answer 1

Answer:

1

If secA+tanA=p, then what is sin A?

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secA =p- tanA

squaring both sides: we get

sec2A=(p−tanA)2

sec2A=p2+tan2A−2ptanA

sec2A−tan2A=p2−2ptanA,since we know the identity(1+tan2A=secA)

hence, 1= p2−2ptanA

tanA= (p2−1)/2p

now,according to right angled triangle, tanA= perpendicular(P)/base(b)

and sinA=perpendicular(P)/hypotnuese(h)

hence we know. P= p2−1,base=2p

so, H= p2+1(calculated by hypotnuese theorem)

now SinA= P/H= (p2−1)/(p2+1)−−ans