Trigonometry

The sum of the squares of sine and cosine of any angle is always 1.. The equation represents the fundamental Pythagorean trigonometric identity, which states that the sum of the squares of sine and cosine for any angle is always 1.

Both tan(45 degrees) and cot(45 degrees) are equal to 1, making their sum 1 + 1 = 2. Option A is incorrect because the two positive terms are added rather than subtracted, meaning they do not cancel out to 0. Option D is a common mistake for those confusing these values with sin(45 degrees).

This is a fundamental Pythagorean trigonometric identity that holds true for all angles, derived from the unit circle where the coordinates satisfy the equation x^2 + y^2 = 1. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Many students confuse this identity with other trigonometric formulas or mistakenly believe it only applies under specific conditions, rather than universally for all angles.
• !Option A is incorrect because the sum of these squares cannot be 0, as the coordinates on a unit circle must always satisfy the radius equation of x squared plus y squared equals 1.
• !Option A is incorrect because the two positive terms are added rather than subtracted, meaning they do not cancel out to 0.
• !Option A is incorrect because 2 sin θ cos θ is the double-angle identity for sin(2θ), not cos(2θ).

Answer each from memory — you'll see instantly whether you're right and why.

Run a focused 10-question mini-mock on Trigonometry and see it stick.