Question

if tan A=3, tan B=1, A and B are acute angle. Find cos(A-B)​

Answer 1

Answer:

( 1 + √3)/2√2

Step-by-step explanation:

Correct Question :-

if tan A=√3, tan B=1, A and B are acute angle. Find cos(A-B)​

Given,

tanA = √3 , tanB = 1

A , B are acute angles.

To Find :-

Value of cos(A - B)

How To Do :-

As they given the values of 'tanA' and 'tanB' we need to find the values of 'angle A and angle B' from that. After obtaining those values we need to find the values of 'cosA , cosB , sinA , sinB' and we need to substitute these values in the formula 'cos(A - B)'.

Formula Required :-

tan60° = √3

tan45° = 1

cos(A - B) = cosA.cosB + sinA.sinB

sin60° = √3/2

sin45° = 1/√2

cos60° = 1/2

cos45° = 1/√2

Solution :-

tanA = √3

tanA = tan60°

Cancelling 'tan' on both sides :-

A = 60°

tanB = 1

tanB = tan45°

Cancelling 'tan' on both sides :-

B = 45°

→ cosA = cos60°

= 1/2

cosB = cos45°

= 1/√2

sinA = sin60°

= √3/2

sinB = sin45°

= 1/√2

cos(A - B) = cosA.cosB + sinA.sinB

=( 1/2 × 1/√2) + (√3/2 × 1/√2)

= 1/2√2 + √3/2√2

=( 1 + √3)/2√2

∴ cos(A - B) = ( 1 + √3)/2√2