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In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. …

In basic trigonometry computes sine, cosine, tangent, and their reciprocal. Calculates arcsin, arccos, and arctan values inside inverse trigonometric equations. Trigonometric identities …

Basic trig identities are formulas for angle sums, differences, products, and quotients; and they let you find exact values for trig expressions.

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prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx

The two formulas of sin squared x are i) sin^2x = 1-cos^2x and ii) sin^2x =(1 - cos 2x)/2.

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The usual convention is that $\sin^2(X)=(\sin(X))^2$. So for your example $1/4$ is correct

Sin 2x formula is one of the double angle formulas in trigonometry. Using this formula, we can find the sine of the angle whose value is doubled.