Question

1) simplify cos ( pie/3 + x ) - sin ( pie/6 - x )
2) prove that cos ( 3pie /4 +x ) - cos(3pie/4-x) = - root 2 sin x
3) prove that sin 18° = root 5-1/4, cos 36° = root 5+1/4.

please answer these questions step by step perfectly.​

Answer 1

Answer:

1) 0

2) -√2sinx (proved)

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Answer 2

Answer:

* Cox (60+2) - Sin (30-x).

= cos60 cosa-sinto sinx-(singo (asx- (6550-sinx)

cos (34 +2) - (0.5 (37-2). - Jisinx

3 (155-+2) = (as (135-2) - - √₂. sinx

* cos((39)-cocx-str(39) sinx- (cos(35), 605 x +sin (35).

sim 2 sin

(85 (90+45) 083x sin (90+16) sina-cosplotus)-cosa-sin

1. sinna sina = -√2 singa. (moved)