Question

(sin A + cos A) (tan A + cot A) = sec A + consecutive A​

Answer 1

Knowing that $tanA = \frac{sinA}{cosA}$, $cotA = \frac{cosA}{sinA}$, opening the brackets:

$Expression = \frac{sin^2A}{cosA} + cosA + sinA + \frac{cos^2A}{sinA}$

Now, combining (LCM) the sin²A term with cosA and cos²A term with sinA, we get:

$Expression = \frac{1}{cosA} + \frac{1}{sinA}$

(Since sin²A + cos²A = 1)

Which, is equal to (by definition):

$= secA + cosecA$

Hence proved.

Answer 2

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