how to find tan &#x2061;<!-- ⁡ --> ( x 2 </mfrac> )

Blericker74

Blericker74

Answered question

2022-07-13

how to find tan ( x 2 ) knowing that cos ( x ) + sin ( x ) = 7 5

Answer & Explanation

verzaadtwr

verzaadtwr

Beginner2022-07-14Added 17 answers

Since
sin x = 2 sin x 2 cos x 2 cos x = cos 2 x 2 sin 2 x 2
so
cos ( x ) + sin ( x ) = 7 5 5 ( cos 2 x 2 sin 2 x 2 ) + 10 sin x 2 cos x 2 = 7 ( cos 2 x 2 + sin 2 x 2 ) 12 sin 2 x 2 10 sin x 2 cos x 2 + 2 cos 2 x 2 = 0 6 tan 2 x 2 5 tan x 2 + 1 = 0 tan x 2 = 5 ± 1 12

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