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Simplify \newlinetan⁡xcsc⁡xcos⁡x\tan x \csc x \cos x

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Full solution

Q. Simplify \newlinetan⁡xcsc⁡xcos⁡x\tan x \csc x \cos x
  1. Understand Identities: Understand the trigonometric identities involved.\newlineThe trigonometric identities that we need to know for this problem are:\newline11. tan⁡x=sin⁡xcos⁡x\tan x = \frac{\sin x}{\cos x}\newline22. csc⁡x=1sin⁡x\csc x = \frac{1}{\sin x}\newlineWe will use these identities to simplify the expression.
  2. Substitute Identities: Substitute the identities into the expression. tan⁡xcsc⁡xcos⁡x=(sin⁡x/cos⁡x)∗(1/sin⁡x)∗cos⁡x\tan x \csc x \cos x = (\sin x / \cos x) * (1 / \sin x) * \cos x
  3. Simplify Expression: Simplify the expression by canceling out terms.\newline(sin⁡x/cos⁡x)∗(1/sin⁡x)∗cos⁡x=(sin⁡x∗1∗cos⁡x)/(cos⁡x∗sin⁡x)(\sin x / \cos x) * (1 / \sin x) * \cos x = (\sin x * 1 * \cos x) / (\cos x * \sin x)\newline=1= 1\newlineThe sin⁡x\sin x and cos⁡x\cos x terms cancel out because they appear in both the numerator and the denominator.

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