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Calculate cos 60° in terms of other trignometric ratios.
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Solution :-
Let ABC be an equilateral triangle whose each side is 2a By Geometry each angle of Triangle is 60° Let AD is perpendicular to BC From Geometry ,
AD bisects Triangle BAC also bisects side BC
So, angle CAD = angle BAD = 30° and CD = BD =a
In a right angle triangle ADC ,
AD² + DC² = AC²
AD² +(a)² = (2a)²
AD² +a² = 4a²
AD² = 4a² - a²
AD² = 3a²
AD = √3a
From Right angle Triangle ADC
We know that ,
cosA = adjacent side toA / hypotenuse
Here the adjacent side is 'a'
Hypotenuse is 2a
So, cos60° = adjacent side/ hypotenuse
cos60° = a/2a
cos60° = 1/2
___________________
Know more :-
Trignometric Identities :-
sin²θ + cos²θ = 1
sec²θ - tan²θ = 1
csc²θ - cot²θ = 1
Trigonmetric relations:-
sinθ = 1/cscθ
cosθ = 1 /secθ
tanθ = 1/cotθ
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
Trigonmetric ratios:-
sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj
cotθ = adj/opp
cscθ = hyp/opp
secθ = hyp/adj
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