Question

solve the given question​

Answer 1

Answer:

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Step-by-step explanation:

ANS 18 :

sin(A-B) = 1/2

=> sin(A-B) = sin(30)

=> A-B = 30 ------------------(1)

cos(A+B) =1/2

=>cos(A+B) = cos(60)

=>A+B = 60 -------------------(2)

Adding (1) and (2) we get,

A-B + A+B = 30+60

=>2A = 90

Therefore A=45 degrees

On putting value of A in equation(2) we get,

45+B=60

Therefore B = 60-45 = 15 degrees

ANS 19:

sin(A+B)=1

=> sin(A+B) = sin(90)

=> A+B = 90 ----------------(1)

cos(A-B)=1

=> cos(A-B) = cos(0)

=>A-B = 0 -------------------(2)

Adding (1) and (2) we get,

A+B + A-B = 90+0

=>2A=90

Therefore A=45 degrees

On putting value of A=45 in equation(1) we get,

45+B=90

=>B=90-45

Therefore B=45 degrees

ANS 20:

tan(A-B) = 1/root(3)

=>tan(A-B) = tan(30)

=> A-B = 30 ----------------(1)

tan(A+B) = root(3)

=>tan(A+B) = tan(60)

=>A+B = 60 ----------------(2)

Adding (1) and (2) we get,

A-B + A+B = 30+60

=>2A=90

Therefore A=45 degrees

putting A=45 in equation (2), we get,

45+B = 60

Therefore B=15 degrees

ANS 21:

cos(A-B) = root(3)/2

=> cos(A-B) = cos(30)

=> A-B = 30 ---------------(1)

sin(A+B) = 1

=>sin(A+B) = sin(90)

=>A+B = 90 ---------------(2)

Adding (1) and (2) we get,

A-B + A+B = 30+90

=> 2A = 120

Therefore A=60 degrees

On putting A=60 in equation (2) we get,

60 + B =90

Therefore B=30 degrees.

Answer 2

Answer:

(18) sin(A-B) = 1/2

=> sin(A-B) = sin(30°)

=> A-B = 30° ------------------(1)

cos(A+B) =1/2

=>cos(A+B) = cos(60°)

=>A+B = 60° -------------------(2)

On adding (1) and (2) we get,

A-B + A+B = 30°+60°

=>2A = 90°

So A=45°

On putting value of A in equation(2) we get,

45+B=60°

Therefore B = 60°-45° = 15°

19) sin(A+B)=1

=> sin(A+B) = sin(90°)

=> A+B = 90° ----------------(1)

cos(A-B)=1

=> cos(A-B) = cos(0°)

=>A-B = 0° -------------------(2)

On adding (1) and (2) we get,

A+B + A-B = 90°+0°

=>2A=90°

Therefore A=45°

On putting value of A=45° in equation(1) we get,

45+B=90°

=>B=90°-45°

Therefore B=45°

(20) tan(A-B) = 1/root(3)

=>tan(A-B) = tan(30°)

=> A-B = 30° ----------------(1)

tan(A+B) = √3

=>tan(A+B) = tan(60°)

=>A+B = 60° ----------------(2)

Adding (1) and (2) we get,

A-B + A+B = 30°+60°

=>2A=90°

Therefore A=45°

putting A=45° in equation (2), we get,

45°+B = 60°

Therefore B=15°

Step-by-step explanation:

(21) cos(A-B) = √3/2

=> cos(A-B) = cos(30°)

=> A-B = 30° ---------------(1)

sin(A+B) = 1

=>sin(A+B) = sin(90°)

=>A+B = 90° ---------------(2)

On adding (1) and (2) we get,

A-B + A+B = 30°+90°

=> 2A = 120°

Therefore A=60°

On putting A=60° in equation (2) we get,

60° + B =90°

Therefore B=30°