यदि sin (A + B) =  और tan (A – B) = 1 है। A और B के मान क्या हैं?

  1. 37,  54
  2. 35.7, 40.7
  3. 50, 10
  4. 52.5, 7.5

Answer (Detailed Solution Below)

Option 4 : 52.5, 7.5
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प्रयुक्त सूत्र:

sin 60°  =  

tan 45° = 1

गणना:

दिया गया है कि,

sin (A + B) = 

⇒ sin (A + B) = sin 60° 

∴ A + B = 60°   ----(1)

साथ ही, दिया है

tan (A – B) = 1 

⇒ tan (A – B) = tan 45°

∴ A – B = 45°  ----(2)

समीकरण (1) और (2) को जोड़ने पर

2 A = 105

A = 52.5

समीकरण (1) से, हमें प्राप्त होता है

B = 7.5

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