Question

If cos (A + B) = 0 and cot(A - B) = √3 then find the value of:

(i) (cos Acos B - sin Asin B)

cot B - cot A
(ii) __________

cos A cot B+1​

Answer 1

Answer:

sinA/sinB = root 3/2.

=》sin^2 A/sin^2 B = 3/4.

=》sin^2 A = 3sin^2 B/4 ...(1)

Again,

cosA/cosB = root5/2

=》cos^2 A = 5cos^2 B/4 ...(2)

Adding (1) and (2),

cos^2 A + sin^2 A = 1 = 5cos^2 B/4 + 3sin^2 B/4 = (5cos^2 B + 3sin^2 B)/4.

=》4 = 5cos^2 B + 3sin^2 B = 5(1-sin^2 B) + 3sin^2 B = 5 - 2sin^2 B.

=》sin B = 1/root 2 = sin 45.so, tan B = tan 45 = 1 ...(3)

Also,

cos B = cos 45 = 1/root 2.

Again, cosA/cosB = cosA/(1/root2) = root 5/2.

=》cosA = root5/root 8,

(Now, by using square- identity), we get:

tan A = root 3/ root 5 ....(4).

Adding (3) and (4),

tan A + tan B = 1 + root 3/root 5 = (root 5 + root 3)/root 5

Answer 2

Congratulations "expert" ʕっ•ᴥ•ʔっ