यदि Tan A Tan B + \(\frac{{\cos x}}{{\cos A\cos B}}\) = 1, तो x = ?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 4)

Answer 1

दिया गया है:

Tan A Tan B + \(\frac{{\cos x}}{{\cos A\cos B}}\) = 1

प्रयुक्त सूत्र:

\(Tan\:\theta={Sin\:\theta\over Cos\:\theta}\)

Cos (a + b)= cos a cos b - sin a sin b

गणना:

Tan A Tan B + \(\frac{{\cos x}}{{\cos A\cos B}}\) = 1

⇒ Tan A Tan B Cos A Cos B + Cos x = Cos A Cos B

⇒ Sin A Sin B + Cos x = Cos A Cos B

⇒ Cos x = Cos A Cos B - Sin A Sin B

⇒ Cos x = Cos (A + B)

⇒ x = A + B

इसलिए, सही उत्तर 'विकल्प 3' है।