Page 44 - modul trigonometri bilingual

Example 3.1

2
Prove the following trigonometric identity (tan + cot ) cos =
cot

Alternative Solutions

The shape of the left segment of the equation is changed so that it is

the same as the shape of the right field.

Left field:

2
(tan + cot ) cos ← Change to the basic shape of the cosine sinus
sin cos
2
= ( + ) cos ← match the denominator
cos sin
sin sin cos cos
2
= ( × + × ) cos
cos sin sin cos
sin sin cos cos
2
= ( + ) cos
cos sin cos sin
2
2
sin + cos
2
2
2
= ( ) cos ← match the denominator sin + cos = 1
cos sin
1
= ( ) cos cos
cos sin
cos
=
sin
= cot

= right field (proven)

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