Question

find the value of sec60°by appropriate method

Answer 1

hope it is correct........

Answer 2

Hey User,

♦ Trigonometric Identities ♦

→ Firstly, sec θ = cosec ( 90° - θ )

=> sec 60° = cosec( 90° - 60° ) = cosec 30° = ( 1 / sin 30° ) = 2

→ Or, sec θ = ( 1 / cos θ ) 

=> sec 60° =  ( 1 / cos 60° ) = ( 1 / 1 / 2 ) = 2

→ Or, if you find these methods inappropriate.. or relative, check the attachment and you'll get how sec 60° is found Geometrically...
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→ In given equilateral ΔABC, all the angles are 60°

We bisect angle A and as we know, angle bisector in an equilateral triangle perpendicularly bisects the opposite side

=> ∠ADC = 90°

Also, since this is equilateral triangle, ∠ACB = 60°

=> sec 60° = sec ∠ACB = [ AC / CD ]

But, CD = 1/2 BC = 1/2 AC

=> sec 60° = [ AC / ( 1/2 AC ) ] = 2
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Here you go √√√