Simplify the expression tan((pi)/(2)-theta)sin theta

Use Complementary Angle Identity: Express tan((pi/2) - theta) using the complementary angle identity for tangent, which states that tan((pi/2) - theta) = cot(theta).Reciprocal of Tangent: Recall that cot(theta) is the reciprocal of tan(theta), so cot(theta) = 1/tan(theta) or cot(theta) = cos(theta)/sin(theta).Substitute and Simplify: Substitute cot(theta) with cos(theta)/sin(theta) in the given expression to get (cos(theta)/sin(theta)) * sin(theta).Simplify the expression by canceling out the sin(theta) in the numerator and the denominator to get cos(theta).

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Simplify the expression
tan((pi)/(2)-theta)sin theta

Simplify the expression $\newline$ $\tan \left(\frac{\pi}{2}-\theta\right) \sin \theta$

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Algebra 2

Simplify expressions using trigonometric identities

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Q. Simplify the expression

\newline

\tan \left(\frac{\pi}{2}-\theta\right) \sin \theta

Use Complementary Angle Identity: Express $\tan\left(\frac{\pi}{2} - \theta\right)$ using the complementary angle identity for tangent, which states that $\tan\left(\frac{\pi}{2} - \theta\right) = \cot(\theta)$ .
Reciprocal of Tangent: Recall that $\cot(\theta)$ is the reciprocal of $\tan(\theta)$ , so $\cot(\theta) = \frac{1}{\tan(\theta)}$ or $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$ .
Substitute and Simplify: Substitute $\cot(\theta)$ with $\frac{\cos(\theta)}{\sin(\theta)}$ in the given expression to get $\left(\frac{\cos(\theta)}{\sin(\theta)}\right) \cdot \sin(\theta)$ .
Substitute and Simplify: Substitute $\cot(\theta)$ with $\frac{\cos(\theta)}{\sin(\theta)}$ in the given expression to get $\left(\frac{\cos(\theta)}{\sin(\theta)}\right) \cdot \sin(\theta)$ . Simplify the expression by canceling out the $\sin(\theta)$ in the numerator and the denominator to get $\cos(\theta)$ .