The process of simplification using Pythagorean identities involves utilizing the Pythagorean theorem's equivalents in trigonometry: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = csc²θ. These identities are incredibly useful in simplifying and resolving trigonometric equations by replacing them with equivalent expressions.
| Topic | Problem | Solution |
|---|---|---|
| None | The expression below simplifies to a constant, a … | Given the expression \(\frac{\cos ^{2} x}{\sin ^{2} x}+\csc x \sin x\) |
| None | Perform the indicated operation and simplify the … | Given the expression is \(\tan x(\csc x-\cot x)\). |
| None | 18. Simplify: $\frac{2 \tan x}{1+\tan ^{2} x}$ | Given expression: \(\frac{2 \tan x}{1+\tan ^{2} x}\) |
| None | 12. \( \cos \theta\left(1+\tan ^{2} \theta\right)… | \( \cos \theta\left(1+\tan ^{2} \theta\right) \) |