If a cot ø + b cosec ø = p and b cote ø + a cosec ø = q then p2 - q2 is equal to______.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. b2 - a2
Given that
If a cot ø + b cosec ø = p ........(1
and b cote ø + a cosec ø = q .......(2
Squaring both sides of the equation and subtracting them
(a cot ø + b cosec ø)2 - (b cote ø + a cosec ø)2 = p2 - q2
then p2 - q2 = a2cot2ø + b2 cosec2ø + 2ab cotø * cosecø - b2cot2ø - a2 cosec2ø - 2ab cotø * cosecø
p2 - q2 = (b2 - a2) (cot2ø + cosec2ø)
p2 - q2 = b2 - a2