How to prove sin^2(theta)+cos^2(theta)=1

May 13, 2025




 fundamental trigonometric identity. It holds true for all values of

θ\theta, and it's one of the most important identities in trigonometry.

It comes directly from the Pythagorean Theorem applied to the unit circle. For any angle θ:




Limit function (x^2-4)/(x-2) as approaches 2

May 12, 2025

 




To find the limit of the function

lim⁡x→2x2−4x−2\lim_{x \to 2} \frac{x^2 - 4}{x - 2}

Step 1: Factor the numerator

x2−4=(x−2)(x+2)x^2 - 4 = (x - 2)(x + 2)

Step 2: Cancel common factors

(x−2)(x+2)x−2=x+2for x≠2\frac{(x - 2)(x + 2)}{x - 2} = x + 2 \quad \text{for } x \ne 2

Step 3: Take the limit of the simplified function

lim⁡x→2x+2=4\lim_{x \to 2} x + 2 = 4

Final Answer:

4\boxed{4}

Calculate the square root 2 using logarithms.

May 11, 2025

Calculate the square root 2 using logarithms.





1. Find the logarithm of 2
2. Devid the logarithm by 2
3. Find the inverse of logarithm.

Final Answer:

2≈1.4125
















\sqrt{2} \approx 1.4125
2the square root of 2 end-root






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