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Question

Mathematics Question on Trigonometric Identities

Choose the correct option. Justify your choice. (sec A + tan A) (1 - sin A)

A

sec A

B

sec A

C

sin A

D

cos A

Answer

cos A

Explanation

Solution

(sec A + tan A) (1 - sin A)

=(1cos A+ sin Acos A)(1−sin A)=\left (\frac{1}{\text{cos A}} +\frac{\text{ sin A}}{\text{cos A}}\right) (1 - \text{sin A})

=[1+sin Acos A](1−sin A)= \left[\frac{1 + \text{sin A}}{\text{cos A}}\right] (1 - \text{sin A})

=1−sin2Acos A= \frac{1 - \text{sin}^2 A }{\text{cos A}}

=cos2Acos A= \frac{\text{cos}^2 A}{\text{cos A}} (By using the identity sin2θ + cos2θ = 1)
= cos A
Hence, option (D) is correct.