Question

If sin (A+B) A) 45° √√3 2 √√3 and cos(A-B) = then A= B) 15⁰ C) 60 [ ] D) 30°​

Answer 1

Answer:

Step-by-step explanation:

sin(A+B)=cos(A-B)=√3/2

∴, sin(A+B)=√3/2

or, sin(A+B)=sin60°

or, A+B=60° --------------(1)

cos(A-B)=√3/2

or, cos(A-B)=cos30°

or, A-B=30° ---------------(2)

Adding (1) and (2) we get,

2A=90°

or, A=45°

Putting in (1) we get,  

45°+B=60°

or, B=15°

∴, A=45°, B=15°

Answer 2

Answer:

sin(A+B)=cos(A-B)=√3/2

∴, sin(A+B)=√3/2

or, sin(A+B)=sin60°

or, A+B=60° --------------(1)

cos(A-B)=√3/2

or, cos(A-B)=cos30°

or, A-B=30° ---------------(2)

Adding (1) and (2) we get,

2A=90°

or, A=45°

Putting in (1) we get,  

45°+B=60°

or, B=15°

∴, A=45°, B=15°

Step-by-step explanation:

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