If sin 3 </msup> &#x2061;<!-- ⁡ --> x

kunyatia33

kunyatia33

Answered question

2022-05-29

If sin 3 x cos 3 x sin x cos x cos x 1 + cot 2 x 2 tan x cot x = 1 where x [ 0 , 2 π ]

Answer & Explanation

Martha Mcclain

Martha Mcclain

Beginner2022-05-30Added 5 answers

Since
sin 3 x cos 3 x sin x cos x cos x 1 + cot 2 x 2 tan x cot x = 1
sin 2 x + sin x cos x + cos 2 x cos x sin 2 x + cos 2 x sin 2 x 2 = 1
sin x cos x | sin x | cos x = 0
which is always true for sin x 0 otherwise it is true for x = 0 , π 2 , 3 π 2 , 2 π
Therefore, since we also need x π 2 , 3 π 2 for tan x and x 0 , 2 π for cot x all the solutions are given by x ( 0 , π ) with x π / 4 and x π / 2.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?