If
`sin A + cos A = p and sec A + cosec A = q ,`
then prove that :
`q(p^(2) - 1) = 2 p`

If sin theta+ cos theta = p and sec theta + cosec theta = q ; show that q(p^2-1) = 2p

If sintheta+costheta=pandsectheta+"cosec"theta=q then prove that q(p^(2)-1)=2p .

if p: q :: r , prove that p : r = p^(2): q^(2) .

Prove that : (sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A

If p and p' are the distances of the origin from the lines x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k "cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).

If p sin^(3)alpha+qcos^(3)alpha=sinalphacosalpha and p sinalpha - q cos alpha=0, then prove that : p^(2)+q^(2)=1

If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , " then" angleR is equal to

Prove that q^^~p -=~ (q to p)

If cosec theta + cot theta = p prove that cos theta = p2-1 / p2 + 1

If log_(5)p = a and log_(2)q=a , then prove that (p^(4)q^(4))/(100) = 100^(2a-1)