Question

Find cos(45° - A) cos(45° - B) - sin (45° - A) sin(45° - B)​

Answer 1

Answer:

HEY HERE IS YOUR ANSWER

cos(45-A+45-B). : cos(A+B)

cos(90-(A+B))

cos(90)cos(A+B)+sin(90)sin(A+B). :

cos(A-B)

O+sin(A+B) :: cos(90)=0,sin(90)=1

sin(A+B)

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Answer 2

L.H.S = cos(45° – A) ·cos(45° – B) – sin(45° – A) · sin(45° – B)

L.H.S = cos(45° – A) ·cos(45° – B) – sin(45° – A) · sin(45° – B) = cos(45° – A + 45° – B)

L.H.S = cos(45° – A) ·cos(45° – B) – sin(45° – A) · sin(45° – B) = cos(45° – A + 45° – B) ∵ cosA . cosB – sinA . sinB

L.H.S = cos(45° – A) ·cos(45° – B) – sin(45° – A) · sin(45° – B) = cos(45° – A + 45° – B) ∵ cosA . cosB – sinA . sinB = cos(90° – (A + B))

L.H.S = cos(45° – A) ·cos(45° – B) – sin(45° – A) · sin(45° – B) = cos(45° – A + 45° – B) ∵ cosA . cosB – sinA . sinB = cos(90° – (A + B)) = cos (A + B) = sin(A + B) = R.H.S.