verify
1-sintheta * costheta * tantheta = cos^2theta
LS = 1 - sinØcosØ(sinØ/cosØ)
= 1 - sin^2 Ø
= cos^2 Ø
= RS
thank you, what does RS and LS stand for?
Right Side --RS
Left Side ???
To verify the identity 1 - sinθ * cosθ * tanθ = cos^2θ, we need to simplify both sides of the equation and show that they are equal.
Let's start with the left-hand side (LHS):
LHS = 1 - sinθ * cosθ * tanθ
We know that tanθ = sinθ / cosθ, so we can substitute that in:
LHS = 1 - sinθ * cosθ * (sinθ / cosθ)
Now, let's simplify this expression:
LHS = 1 - sinθ * sinθ
Using the trigonometric identity sin^2θ + cos^2θ = 1, we can rewrite the expression as:
LHS = 1 - (1 - cos^2θ) (since sin^2θ = 1 - cos^2θ)
LHS = 1 - 1 + cos^2θ
LHS = cos^2θ
Now, let's simplify the right-hand side (RHS):
RHS = cos^2θ
As we can see, the simplified left-hand side (LHS = cos^2θ) is equal to the right-hand side (RHS = cos^2θ). Therefore, the identity 1 - sinθ * cosθ * tanθ = cos^2θ is verified.
In summary, by simplifying both sides of the equation using trigonometric identities and substitution, we showed that the left-hand side (LHS) is equal to the right-hand side (RHS), thus verifying the given identity.