Simplify Using Pythagorean Identities

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.

The problems about Simplify Using Pythagorean Identities

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)…	$\cos θ (1 + \tan^{2} θ)$