I need to choose the next step for (secx-sin^2 x sec x) and the rule that applie

Question

I need to choose the next step for (secx-sin^2 x sec x) and the rule that applies to that particular step. It would be very helpful if someone could continue solving the identity until it matches the right side. Thank You.

Prove the identity. cos r Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the corresponding question mark. Statement Rule sec x -sin x secx Rule Click here to validate this line; click on Check below to submit your answen.

Explanation / Answer

sec x - sin^2 x sec x = cos x

manipulating left hand side

sec x ( 1 - sin^2 x )

1 - sin^2 x = cos^2 x ( pythagorean identity )

so we have now ,

sec x ( cos^2 x )

sec x = 1/ cos x ( reciprocal identity )

1/ cos x * cos^2 x

= cos x

which is right side

hence proved !

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