prove
cos squared B- sin squared B= 2cos squared B -1
cos^2 B - sin^2 B = 2cos^ B - 1
LS
= cos^2 B - (1 - cos^2 B)
= 2cos^2 B - 1
= RS
substitute 1 - cos^2B for sin^2 B
To prove the equation cos²(B) - sin²(B) = 2cos²(B) - 1, we will use the trigonometric identity for cosine of double angle.
The double angle formula for cosine is:
cos(2θ) = cos²(θ) - sin²(θ)
Now, let's substitute θ with B/2:
cos(B) = cos²(B/2) - sin²(B/2)
Since we want to prove cos²(B) - sin²(B) = 2cos²(B) - 1, we need to show that cos(B) is equal to 2cos²(B/2) - 1.
Let's express cos(B) in terms of B/2 using the double angle formula:
cos(B) = cos(2(B/2))
cos(B) = 2cos²(B/2) - 1
This confirms the equation cos²(B) - sin²(B) = 2cos²(B) - 1.
Thus, we have proved the given equation using the double angle formula for cosine.