Question : Which of the following is equal to $[\frac{\cos heta}{\sin heta}+\frac{\sin heta}{\cos heta}]$?
Option 1: $\operatorname{cosec} heta \sec heta$
Option 2: $\sec heta an heta$
Option 3: $\operatorname{cosec} heta an heta$
Option 4: $\cot heta \sec heta$

Question

Question : Which of the following is equal to $[\frac{\cos heta}{\sin heta}+\frac{\sin heta}{\cos heta}]$?

Option 1: $\operatorname{cosec} heta \sec heta$

Option 2: $\sec heta an heta$

Option 3: $\operatorname{cosec} heta an heta$

Option 4: $\cot heta \sec heta$

Team Careers360 · Accepted Answer

Correct Answer: $\operatorname{cosec} heta \sec heta$

Solution : Given: The expression is $[\frac{\cos heta}{\sin heta}+\frac{\sin heta}{\cos heta}]$.
We know the trigonometric ratios, $\frac{1}{\sin heta} =\operatorname{cosec} heta$ and $\frac{1}{\cos heta} = \sec heta$ and the trigonometric identity, $\sin^2 heta+\cos^2 heta=1$
$[\frac{\cos heta}{\sin heta}+\frac{\sin heta}{\cos heta}]$
$=\frac{\sin^2 heta+\cos^2 heta}{\sin heta imes \cos heta}$
$=\frac{1}{\sin heta imes \cos heta}=\operatorname{cosec} heta \sec heta$
Hence, the correct answer is $\operatorname{cosec} heta \sec heta$.

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Question : Which of the following is equal to [cos⁡θsin⁡θ+sin⁡θcos⁡θ]?Option 1: cosecθsec⁡θOption 2: sec⁡θtan⁡θOption 3: cosecθtan⁡θOption 4: cot⁡θsec⁡θ

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Question : Which of the following is equal to $[\frac{\cos θ}{\sin θ} + \frac{\sin θ}{\cos θ}]$ ?
Option 1: $cosec θ \sec θ$
Option 2: $\sec θ \tan θ$
Option 3: $cosec θ \tan θ$
Option 4: $\cot θ \sec θ$