Solve the given trigonometric equation 3 cos x 4 sin x 5 ........

Mathematics (NDA) Trigonometry

Solve the given trigonometric equation 3 cos x + 4 sin x = 5 ?

2nπ + 2tan^-1(1/3)

nπ + 2tan^-1(1/2)

2nπ + 2tan^-1(1/4)

2nπ + 2tan^-1(1/2)

3 cos x + 4 sin x = 5

3(1-tan² x/2)/1+tan² x/2 + 4(2 tan x/2)/1+ tan² x/2 =5

3-3tan² x/2 /1+tan² x/2 + 8 tan x/2 /1+tan² x/2 =5

3-3tan² x/2 +8 tan x/2 =5 +5 tan² x/2

8tan² x/2 -8 tan x/2 +2 =0

4tan² x/2 -4tan² x/2 +1=0

(2tan x/2 -1 )²=0

2tan x/2 -1 =0

tan x/2 =1/2

x/2 =tan^-1(1/2)

x=2nπ + 2tan^-1(1/2)

Submit Error