Trigonometric Identify: 1 + cos &#x2061;<!-- ⁡ --> <mr

Raul Walker

Raul Walker

Answered question

2022-07-04

Trigonometric Identify: 1 + cos x sin x = cot x 2

Answer & Explanation

furniranizq

furniranizq

Beginner2022-07-05Added 20 answers

Notice cos x = cos 2 ( x / 2 ) sin 2 ( x / 2 ) and sin x = 2 sin ( x / 2 ) cos ( x / 2 ). Thus,
1 + cos x sin x = 1 + cos 2 ( x / 2 ) sin 2 ( x / 2 ) 2 sin ( x / 2 ) cos ( x / 2 ) = 2 cos 2 ( x / 2 ) 2 sin ( x / 2 ) cos ( x / 2 ) = cos ( x / 2 ) sin ( x / 2 ) = cot ( x / 2 )
Palmosigx

Palmosigx

Beginner2022-07-06Added 4 answers

cot ( x / 2 ) = cos ( x / 2 ) sin ( x / 2 ) = 2 cos 2 ( x / 2 ) sin ( x ) = cos ( x ) + 1 sin ( x )

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