Question

Find angle B if tan (A-B)=1/root 3 and sinA=root 3/2. Also find cosB(A,B less than 90°

Answer 1

Answer:

Step-by-step explanation:

Given that,

A, B less than 90°.They are acute angles.

tan ( A - B ) = 1 / √3 and sin A = √3 / 2

tan ( A - B ) = 1 / √3 = tan 30° and sin A = √3 / 2 = sin 60°

A - B = 30° ----eq ( 1 ) ( say ) and A = 30°

On substituting, A = 30° in eq ( 1 ) ,we have

30° - B = 30°

B = 30° + 30°

B = 60°.

∴ cos B = cos 60° = 1 / 2 is the answer.