cos pie by 4 plus theta cos pie by 4 minus theta equal to root 2 cos theta
Answer (1)
1st Nov, 2024
The problem is thus treated in steps:
We are given that:
cos(π/4 + θ) + cos(π/4 - θ) = √2 cosθ
We shall consider the left-hand side (LHS):
The sum and difference formulas for cosine are useful here:
cos(A + B) = cosA * cosB - sinA * sinB
cos(A - B) = cosA * cosB + sinA * sinB
Substituting into our equation we get:
LHS = [cos(π/4) * cosθ - sin(π/4) * sinθ] + [cos(π/4) * cosθ + sin(π/4) * sinθ]
Now we simplify:
LHS = 2 cos(π/4) cosθ
cos(π/4) = 1/√2. Thus:
LHS = 2(1/√2) cosθ
LHS = √2 cosθ.
Hence, LHS = RHS.
So we have proved that the given equation stands correct.
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