Q1. What is the value of sin squared theta plus cos squared theta?
✔ The fundamental identity states the sum equals one.
Q2. If sin theta is 0.6, what is cos squared theta?
✔ Square 0.6 to get 0.36, subtract from 1.
Q3. Which equation is NOT a valid identity?
✔ Sine and cosine must be squared to sum to one.
Show transcript
[Slide 1] Why These Identities Exist
Think of a right-angled triangle. These identities connect the sides using Pythagoras theorem. They hold true for any valid angle.
[Slide 2] The Main Identity Formula
This is the most important identity you must remember. It states that the sum of squares of sine and cosine is one.
[Slide 3] Solving with Real Numbers
Suppose sine of theta equals three-fifths. We substitute this into our identity to find cosine. This makes solving problems very easy.
[Slide 4] Calculating the Result
Subtract nine twenty-fifth from one to get sixteen twenty-fifth. Taking the square root gives us four-fifths for cosine.
[Slide 5] Avoid This Common Mistake
Many students forget to square the terms before adding. Remember the identity requires squares on both trig functions.
[Slide 6] Quick Recap for Boards
Remember this formula is key for your board exams. Practice substituting values carefully to avoid errors.