Question

if sin a equal to 1 by 2 and cos B equal to 1 by 2 what is is the value of brackets tan a minus tan b ) / (1+tan a tan b)​

Answer 1

if sin a equal to 1 by 2 and cos B equal to 1 by 2 what is is the value of brackets tan a minus tan b ) / (1+tan a tan b)

sinA = 1/2

A = 30°

cosB = 1/2

B = 60°

tanA = tan30 = 1/√3

tanB = tan60 = √3

tanAtanB = tan30*tan60 = 1/√3 * √3 = 1

tanA - tanB

= 1/√3 - √3

= (1-3)/√3

= -2/√3

1+tanAtanB

= 1+1

= 2

Hence,

(tanA-tanB)/(1+tanAtanB)

= (-2/√3)/(2)

= -1/√3

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