verify the identity.\n( \tan \theta cdot cos \theta cdot csc \theta = 1 )\nwhich of the following four…

verify the identity.\n( \tan \theta cdot cos \theta cdot csc \theta = 1 )\nwhich of the following four statements establishes the identity?\na. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{sin \theta}{cos \theta} cdot cos \theta cdot \frac{1}{sin \theta}=1 )\nb. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{cos \theta}{sin \theta} cdot cos \theta cdot \frac{1}{cos \theta}=1 )\nc. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{sin \theta}{cos \theta} cdot cos \theta cdot \frac{1}{cos \theta}=1 )\nd. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{cos \theta}{sin \theta} cdot cos \theta cdot \frac{1}{sin \theta}=1 )

verify the identity.\n( \tan \theta cdot cos \theta cdot csc \theta = 1 )\nwhich of the following four statements establishes the identity?\na. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{sin \theta}{cos \theta} cdot cos \theta cdot \frac{1}{sin \theta}=1 )\nb. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{cos \theta}{sin \theta} cdot cos \theta cdot \frac{1}{cos \theta}=1 )\nc. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{sin \theta}{cos \theta} cdot cos \theta cdot \frac{1}{cos \theta}=1 )\nd. ( \tan \theta cdot cos \theta cdot csc \theta=\frac{cos \theta}{sin \theta} cdot cos \theta cdot \frac{1}{sin \theta}=1 )

Answer

Explanation:

Step1: Recall trigonometric identities

Recall that (\tan\theta=\frac{\sin\theta}{\cos\theta}) and (\csc\theta = \frac{1}{\sin\theta}).

Step2: Substitute identities into the left - hand side

Substitute (\tan\theta=\frac{\sin\theta}{\cos\theta}) and (\csc\theta=\frac{1}{\sin\theta}) into (\tan\theta\cdot\cos\theta\cdot\csc\theta). We get (\frac{\sin\theta}{\cos\theta}\cdot\cos\theta\cdot\frac{1}{\sin\theta}).

Step3: Simplify the expression

Cancel out (\sin\theta) and (\cos\theta) terms. (\frac{\sin\theta}{\cos\theta}\cdot\cos\theta\cdot\frac{1}{\sin\theta}=\frac{\sin\theta\times\cos\theta\times1}{\cos\theta\times\sin\theta}=1)

Answer:

A. (\tan\theta\cdot\cos\theta\cdot\csc\theta=\frac{\sin\theta}{\cos\theta}\cdot\cos\theta\cdot\frac{1}{\sin\theta}=1)