QuestionExample 4: Prove
LS
RS
Studdy Solution
STEP 1
1. We are given the equation and need to prove it.
2. We will manipulate both sides of the equation to show they are equal.
3. We will use trigonometric identities to simplify the expressions.
STEP 2
1. Simplify the Right Side (RS) of the equation.
2. Compare the simplified Right Side with the Left Side (LS).
STEP 3
Start by simplifying the Right Side (RS): .
First, recall the identity for :
Substitute this identity into the RS:
This simplifies to:
STEP 4
Combine the terms over a common denominator:
Use the Pythagorean identity:
Substitute this into the expression:
Simplify by canceling :
STEP 5
Now, compare the simplified Right Side (RS) with the Left Side (LS):
The simplified RS is , which matches the LS.
Since both sides are equal, the equation is proven:
Was this helpful?