Question

Simplify: \( \sin(x + y) \sec x \sec y = \)

• A. \( \cos x \cos y \)
• B. \( \tan x - \tan y \)
• C. \( \cos x + \cos y \)
• D. \( \tan x + \tan y \)

Hint:

Composite Angle with Trigonometric Multipliers}
Use sum of angles identity for sine
Apply trigonometric reciprocals like \( \sec = \frac{1}{\cos} \)
Always simplify carefully to avoid algebraic errors

Answer 1

The Correct Option is D

Using identity: \[ \sin(x+y) = \sin x \cos y + \cos x \sin y \] Multiplying by \( \sec x \sec y \): \[ \sin(x+y) \sec x \sec y = \frac{\sin x}{\cos x} + \frac{\sin y}{\cos y} = \tan x + \tan y \]