AP TET Paper 2 Math and Science Model Paper 2

Concept:The expression is simplified using standard trigonometric identities, primarily $\sec A = \frac{1}{\cos A}$, $\tan A = \frac{\sin A}{\cos A}$, and $1 - \sin^2 A = \cos^2 A$.Explanation:Start with the given expression: $(\sec A + \tan A)(1 - \sin A)$.Substitute $\sec A = \frac{1}{\cos A}$ and $\tan A = \frac{\sin A}{\cos A}$.Then the expression becomes $\left(\frac{1}{\cos A} + \frac{\sin A}{\cos A}\right)(1 - \sin A)$.Combine the terms inside the brackets: $\frac{1 + \sin A}{\cos A}$.Now multiply by $(1 - \sin A)$: $\frac{(1 + \sin A)(1 - \sin A)}{\cos A}$.Use the algebraic identity $(a + b)(a - b) = a^2 - b^2$: $(1 + \sin A)(1 - \sin A) = 1 - \sin^2 A$.So the expression becomes $\frac{1 - \sin^2 A}{\cos A}$.Apply the identity $1 - \sin^2 A = \cos^2 A$: $\frac{\cos^2 A}{\cos A}$.Cancel $\cos A$ in the numerator and denominator to get $\cos A$.Thus, $(\sec A + \tan A)(1 - \sin A) = \cos A$.Answer:$\cos A$Hence, the correct option is B.