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AC ² = a² + a²

=2a²

AC = √2a²

sin 45° = opp/ hyp = a / √2a ( a will be cancelled )

sin 45°= 1/√2

cos 45° = adj/ hyp = 1/ √2

tan 45° = 1

cosec 45 ° = √2

sec 45° = √2

cot 45° = 1

RATIOS OF 60° AND 30°

consider an equilateral Δ ABC with side a .

ΔABC AB = AC = a, AD ⊥ BC , BD = DC = a / 2 , AD = √3/ 2, ∠C = 60°

sin 60 ° = opp / hyp = √3a/ 2 / a ( a will be cancelled )

sin 60° = √3/2

cos 60° = 1/2

tan 60° = √3

cosec 60° = 2/√3

sec 60° = 2

cot 60° = 1/√3

ratios 30°

right angle Δ ABC ∠ A = 30° , AB = √3/2 , BC = a / 2 , AC = a

sin 30°= 1/2

cos 30°= √3/2

tan 30° = 1/ √3

cosec 30°= 2

sec 30°= 2/√3

cot 30° = √3