Cos (A – B) = 1/2; Sin B = 1/√2, then the value of A.A) 15° B)

1.	Cos (A – B) = 1/2; Sin B = 1/√2, then the value of A.A) 15° B) 105° C) 90° D) 60°
Answer» Correct option is: B) 105° We have cos (A-B) = \(\frac 12\) = cos \(60^\circ\) = A - B = \(60^\circ\)....(1) And sin B = \(\frac 1{\sqrt2}\) = sin \(45^\circ\) = B = \(45^\circ\) \(\therefore\) A- \(45^\circ\) = \(60^\circ\) (From (1)) = A = \(60^\circ\) + \(45^\circ\) = \(105^\circ\) Correct option is: B) 105°

Cos (A – B) = 1/2; Sin B = 1/√2, then the value of A.A) 15° B) 105° C) 90° D) 60°

Answer»

Correct option is: B) 105°

We have

cos (A-B) = \(\frac 12\) = cos \(60^\circ\)

= A - B = \(60^\circ\)....(1)

And sin B = \(\frac 1{\sqrt2}\) = sin \(45^\circ\)

= B = \(45^\circ\)

\(\therefore\) A- \(45^\circ\) = \(60^\circ\) (From (1))

= A = \(60^\circ\) + \(45^\circ\) = \(105^\circ\)

Correct option is: B) 105°