Question

If secB +tana=P then find the value of sinB in terms of 'P'​

Answer 1

Answer:

SinB=(p2−1)/(p2+1)

Step-by-step explanation:

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 SinB= P/H= ( p2−1)/(p2+1)−−ans