(sec $\theta$ + tan $\theta$) (1 – sin $\theta$) is equal to ______.

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(sec $\theta$ + tan $\theta$) (1 – sin $\theta$) is equal to cos $\theta$. Explanation: sec $\theta$ = 1/cos $\theta$ tan $\theta$ = sin $\theta$/cos $\theta$ Substituting these into the first bracket: `(1/cos $\theta$ + sin $\theta$/cos $\theta$) (1 - sin $\theta$) ((1 + sin $\theta$)/cos $\theta$) (1 - sin $\theta$) ((1 + sin $\theta$) (1 - sin $\theta$))/cos $\theta$` Using the Difference of Squares formula: (1^2 - sin^2 $\theta$)/cos $\theta$ = (1 - sin^2 $\theta$)/cos $\theta$ Apply the Pythagorean Identity: = cos^2 $\theta$/cos $\theta$ Divide cos2 $\theta$ by cos $\theta$ cos $\theta$

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