How to convert $\sec$ to $\cos$?

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Question

Prove that sin theta minus cos theta + 1 by sin theta + cos theta minus 1 equal to 1 by sec theta minus tan theta

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Answer 1

$\sec$ can be converted to $\cos$ by using the formula $\sec=\frac{1}{cos}$.

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How to convert $\sec$ to $\cos$?

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Prove that sin theta minus cos theta + 1 by sin theta + cos theta minus 1 equal to 1 by sec theta minus tan theta

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Question : $\frac{\sin ^2 \theta}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}=$?
Option 1: $\operatorname{cosec}\theta$
Option 2: $\sec\theta$
Option 3: $2\cos\theta$
Option 4: $2\sec\theta$

Question : The value of $\sec x - \cos x = $?
Option 1: $\tan x \sin x$
Option 2: $\sec x \tan x$
Option 3: $\tan x \cos x$
Option 4: $\sec x \cos x$

Question : $\frac{\cos \theta}{\sec \theta-1}+\frac{\cos \theta}{\sec \theta+1}$ is equal to :

Option 1: $2 \sec ^2 \theta$
Option 2: $2 \cot ^2 \theta$
Option 3: $2 \cos ^2 \theta$
Option 4: $2 \sin ^2 \theta$