Question

given sin A = √3/2 and cos B = 1/2 ,then the value of tan (A-B) is​

Answer 1

Step-by-step explanation:

sinA=root3/2 therefore A=60

cosB=1/2 therefore B=30

tan(60-30)=tan(30)=1/root3

Answer 2

Trigonometry: Trigonometry is the study of angles and relations between angles and their sin, cos, tan, cosec, sec, cot ratios. There are many formulae for calculations:

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec²A - cot²A = 1

• sin2A = 2 sinA cosA

• cos2A = cos²A - sin²A

• tan2A = 2 tanA / (1 - tan²A)

tan(A - B) = 1/√3

EXPLANATION:

Method 1.

Given, sinA = √3/2, i.e., A = 60°

cosB = 1/2, i.e., B = 30°

Now, tan(A - B)

= tan(60° - 30°)

= tan30°

= 1/√3

Method 2.

Given, sinA = √3/2, i.e., A = 60° or, tanA = √3

cosB = 1/2, i.e., B = 30° or, tanB = 1/√3

Now, tan(A - B)

= (tanA - tanB)/(1 + tanA tanB)

= (√3 - 1/√3)/(1 + √3 * 1/√3)

= {(3 - 1)/√3}/(1 + 1)

= (2/√3)/2

= 1/√3