How can I solve these two simultanious trigonometric equations?? sin x cos y=1/4 and 3 tan x=tan y

Hayley Mcclain

Hayley Mcclain

Answered question

2022-11-11

How can I solve these two simultanious trigonometric equations?? sin x cos y = 1 4 and 3 tan x = tan y
I tried to make it of the form of compound/ allied angles like sin ( x + y ) but failed.
Please give me some hint.
Thanks.

Answer & Explanation

avuglantsaew

avuglantsaew

Beginner2022-11-12Added 15 answers

As you asked for the hint, here is the one:
sin x cos y = 1 4 and 3 tan x = tan y
If you transform the second equation, you willl get:
3 tan x = tan y 3 sin x cos y sin y cos x = 0
Using sin x cos y = 1 4 , you will get sin y cos x = 3 4 and sin x cos y = 1 4
sin ( x + y ) = 1 and sin ( x y ) = 1 2

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