Find solution: If (3 sec x+csc x)sin =5cos 2x, calculate z=tan x+sec x

makeupwn

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2022-08-15

Find solution:
If  ( 3 sec x + csc x ) sin x = 5 cos 2 x , calculate  z = tan x + sec x

Answer & Explanation

kidoceanoe

kidoceanoe

Beginner2022-08-16Added 15 answers

Put y = π / 2 x. Then cos x = sin y, sin x = cos y and 1 z = cos x 1 + sin x = sin y 1 + cos y = tan y 2 . Then sin y = 2 z z 2 + 1 , cos y = z 2 1 z 2 + 1 and
3 ( z 2 1 ) z 2 + 1 + 2 z z 2 + 1 = 5 ( 2 z z 2 + 1 ) 3 ,
or 3 z 6 + 2 z 5 + 3 z 4 36 z 3 3 z 2 + 2 z 3 = 0. Mathcad yieds that four roots of this equation are not real and other two are z 1 .50330721831204403873 and z 2 1.9868580533252213137

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