Trigonometric identities: 1 + cos &#x2061;<!-- ⁡ --> (

rmd1228887e

rmd1228887e

Answered question

2022-07-14

Trigonometric identities: 1 + cos ( a ) 1 cos ( a ) + 1 cos ( a ) 1 + cos ( a ) = 2 + 4 cot 2 ( a )

Answer & Explanation

Jaelynn Cuevas

Jaelynn Cuevas

Beginner2022-07-15Added 16 answers

Simplify:
1 + cos a 1 cos a + 1 cos a 1 + cos a ( 1 + cos a ) 2 + ( 1 cos a ) 2 ( 1 cos a ) ( 1 + cos a )
The denominator is the difference of two squares, expand the numerator:
2 + 2 cos 2 a 1 cos 2 a 2 ( 1 + cos 2 a ) sin 2 a 2 sin 2 x + 2 cos 2 x sin 2 x 2 csc 2 x + 2 cot 2 x   2 ( 1 + cot 2 x ) + 2 cot 2 x 2 + 4 cot 2 x

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