Question

If tan A = 1 and tan B = 3; evaluate:
(i) cos A cos B - sin A sin B.
(ii) sin A cos B + cos A sin B.​

Answer 1

Step-by-step explanation:

tanA =1

tanB =3

sinA/cosA =1

sinB/cosB =3

sinA =1

cosA =1

sinB= 3

cosB =1

(i) cosAcosB -sinAsinB

=(1)(1) -(1)(3)

=1-3

=(-2)

(ii) sinAcosB + cosAsinB

=(1)(1) + (1)(3)

=1+3

=4

Answer 2

Answer:

Given,

tan A=1

⇒A=45°

 tan B=  √3

​ ⇒B = 60°

 cos A cos B − sin A sin B

=cos 45 cos 60 − sin 45 sin 60

= $\frac{1}{\sqrt{2} } \times \frac{1}{2} - \frac{1}{\sqrt{2} } \times\frac{\sqrt{3} }{2} \\\\\frac{1-\sqrt{3} }{2\sqrt{2} }$