Question

If cot B = 3, find the value of cos2B - sin2B2cos B. sin B.

Answer 1

Step-by-step explanation:

Given cotAcotB=2

⇒

sinA

cosA

.

sinB

cosB

=2

⇒cosAcosB=2sinAsinB

⇒cos(A−B)=cosAcosB+sinAsinB=3sinAsinB

⇒cos(A+B)=cosAcosB−sinAsinB=sinAsinB

Now cos(A+B).sec(A−B)=

cos(A−B)

cos(A+B)

=

3sinAsinB

sinAsinB

=

3

1