Question

If a=b cosec theta, c=d cot theta. Prove that a²/b²-c²/d²=1

Answer 1

Answer:

PS is perpendicular to QR

So, using Pythagoras theorem in ΔPSR

PR² = PS² + RS²

⇒ PS² = PR² - RS²

⇒ PS² = b² - d² .........(1)

Now, using Pythagoras theorem in ΔPSQ

PQ² = PS² + QS²

⇒ PS² = PQ² - QS²

⇒ PS² = a² - c² .........(2)

From equation (1) and equation (2)

⇒ b² - d² = a² - c²

⇒ a² - b² = c² - d²

⇒ (a + b)(a - b) = (c + d)(c - d)

Hence Proved.

Answer 2

Answer:

Step-by-step explanation:

PS is perpendicular to QR

So, using Pythagoras theorem in ΔPSR

PR² = PS² + RS²

⇒ PS² = PR² - RS²

⇒ PS² = b² - d² .........(1)

Now, using Pythagoras theorem in ΔPSQ

PQ² = PS² + QS²

⇒ PS² = PQ² - QS²

⇒ PS² = a² - c² .........(2)

From equation (1) and equation (2)

⇒ b² - d² = a² - c²

⇒ a² - b² = c² - d²

⇒ (a + b)(a - b) = (c + d)(c - d)