Question

Sin(45+theta)×sin(45-theta)

Answer 1

Step-by-step explanation:

sin(45+theta)-cos(45-theta)

[Sin(90-x) = cos x]

=sin(45+theta)-sin(90-(45-theta))

=sin(45+theta)-sin(45+theta))

=0

Answer 2

Answer:

(cos 2∆)/2

Step-by-step explanation:

Sin(A+B)= sinAcosB+sinBcosA

Sin(A-B)= sinAcosB-sinBcosA

A=45;B= theta[I will denote it like this ∆]

Sin 45=cos 45= 1/√2

So,given becomes,

=(Cos∆/√2+sin∆/√2)*(cos∆/√2-sin∆/√2)

{(a+b)(a-b)=a^2-b^2}

=1/2(cos square ∆- sin square ∆)

[Cos 2theta= cos square theta - sin square theta]

=1/2 cos 2∆