Question

psec theta - btan theta=a
qsec theta + atan theta=b
Options:
1)a2 + b2 = p2 + q2
2)a2+p2=b2+q2
3)a2-q2=p2-b2
4)a2-b2=q2+p2

Answer 1

Answer:

psec theta = a + btan theta

p2sec2 theta = a2 + b2 tan2 theta + 2ab tan theta (1)

qsec theta = b - atan theta

q2 sec2 theta = b2 + a2 tan2 theta - 2ab tan theta (2)

eq.(1) + eq. (2)

(p2 + q2) sec2 theta = (a2 + b2) + (a2 + b2) tan2 theta

(p2 + q2) sec2 theta = (a2 + b2) (1 + tan2 theta)

(p2 + q2) sec2 theta = (a2 + b2) sec2 theta

p2 + q2 = a2 + b2