Question

Find the value of A and B if sin( A-B) = ½ and cos( A+B) = ½

Answer 1

Answer:

it's easy man see we know that sin 30° = 1/2 and cos 60°= 1/2 so substitute it and the next is

sin(A-B) = 30° this is equation 1

cos(A+B) = 60° this is equation 2

add equation 1 and 2

it will be 2A= 90°

A= 45 °

the put the value of A in equation 1

45 - B= 30°

-B = -15°

minus cancel

B = 15°

therefore the value of A = 45° and the value of B = 15 °

Answer 2

Answer:

here,

sin(A - B) = ½.

or,

sin(A - B) = Sin 30°

so , A - B = 30 ° ....... 1

ALSO

COS( A + B) = ½

OR,

COS( A + B) = COS60°

=> A + B = 60° ..........2

ON adding and subtracting 1 and 2

we get

A = 45° and

B = 15°

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