Solve this equation;
If sin x = 3/5 and x is acute find the value of tan2x, cos2x and sin2x
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Answer:
tan 2x = 24 / 7
cos 2x = 7 / 25
sin 2x = 24 / 25
Step-by-step explanation:
sin x = opposite / hypotenuse = 3 / 5
=> x is an angle in a 3 : 4 : 5 right angle triangle
=> cos x = 4 / 5 and tan x = 3 / 4
tan 2x = ( 2 tan x ) / ( 1 - tan² x )
= ( 2 × 3/4 ) / ( 1 - (3/4)² )
= ( 3/2 ) / ( 1 - 9/16 )
= ( 3×8 ) / ( 16 - 9 ) [ multiplied numerator and denominator by 16 ]
= 24 / 7
cos 2x = cos² x - sin² x
= (4/5)² - (3/5)²
= 16/25 - 9/25
= 7 / 25
sin 2x = 2 cos x sin x
= 2 × (4/5) × (3/5)
= 24 / 25
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