Question

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

Answer 1

Step-by-step explanation:

secB =p- tanB

squaring both sides: we get

sec2B=(p−tanB)2

sec2B=p2+tan2B−2ptanB

sec2B−tan2B=p2−2ptanB ,since we know the identity( 1+tan2B=secB)

hence, 1= p2−2ptanB

tanB= (p2−1)/2p

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

and sinB=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