Question

17. If A = B = 45°, verify that:
cos (A - B) = cos A cos B + sin A sin B​

Answer 1

Answer:

Given ∠A=∠B=45

∘

sin(A+B)=sin(45

∘

+45

∘

)=sin90

∘

=1

sinAcosB+sinBcosA=sin45

∘

cos45

∘

+sin45

∘

cos45

∘

=2sin45

∘

cos45

∘

=2×

2

1

×

2

1

=1

⟹sin(A+B)=sinAcosB+cosAsinB

Answer 2

Step-by-step explanation:

cos(A-B) =cos (45-45)= cos 0

cos 0 =1

LHS =1

cosA cosB + sinA sinB =

cos A cosB= 1/√2*1/√2=1/2

sinA sinB = 1/√2*1/√2= 1/2

1/2+1/2=1

RHS=1

LHS=RHS hence verified