Question

if tan a + b equal to root 3 and tan a minus b equal to 1 by root 3 , 0 less tha n a+b less than or equal to 90,a less than b find a and b​

Answer 1

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GIVEN THAT ,

tan ( a + b ) = √3

but we know that Tan 60° = √ 3

This is possible only when a + b = 60

∴ a + b = 60 ....[1]

Tan ( a - b ) = 1 / √3

we know that tan 30° = 1/√3

∴ a - b = 30....[2]

adding equations one and two

a - b + a + b = 30 + 60

2a = 90

∴ a = 45°

a +  b = 60

b = 60 - 45 [ transposing the value of a from L.H.S to R.H.S]

∴ b = 15°

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Answer 2

Step-by-step explanation:

GIVEN THAT ,

tan ( a + b ) = √3

but we know that Tan 60° = √ 3

This is possible only when a + b = 60

∴ a + b = 60 ....[1]

Tan ( a - b ) = 1 / √3

we know that tan 30° = 1/√3

∴ a - b = 30....[2]

adding equations one and two

a - b + a + b = 30 + 60

2a = 90

∴ a = 45°

a +  b = 60

b = 60 - 45 [ transposing the value of a from L.H.S to R.H.S]

∴ b = 15°GIVEN THAT ,

tan ( a + b ) = √3

but we know that Tan 60° = √ 3

This is possible only when a + b = 60

∴ a + b = 60 ....[1]

Tan ( a - b ) = 1 / √3

we know that tan 30° = 1/√3

∴ a - b = 30....[2]

adding equations one and two

a - b + a + b = 30 + 60

2a = 90

∴ a = 45°

a +  b = 60

b = 60 - 45 [ transposing the value of a from L.H.S to R.H.S]

∴ b = 15°