Question

if tan a=4/5,find 4 cos 2a-5 sin 2a.

Answer 1

Answer:

- 4

Step-by-step explanation:

tan a=4/5,find 4 cos 2a - 5 sin 2a.

cosa = 5/√41 , sina 4/√41

cos2a = 9/41 , sin2a = 40/41

4 cos 2a - 5 sin 2a = (36 - 200) /41 = - 164/41 = - 4

.

Answer 2

cos2a=1-tan^2a/1+tan^2a

sin2a=2tana/1+tan^2 a

cos 2a =(1-(4/5)^2)/1+(4/5)^2=9/41

sin2a =2(4/5)/1+(4/5)^2=40/41

4cos 2a-5sin2a=4(9/41)-5(40/41)

=-164/41

=-4