What is $\sqrt{(1-sinA)}\sqrt{(1+sinA)}$?
Answer & explanation
Correct answer: option 4
$\sqrt{(1-sinA)}\sqrt{(1+sinA)}$
= $\sqrt{1 - sin^2A}$ (1 - sin²A = cos²A)
= $\sqrt{cos^2A}$
= cosA
Alternatively,
take A = 45°
$\sqrt{(1-sinA)}\sqrt{(1+sinA)}$
= $\sqrt{(1-sin45)}\sqrt{(1+sin45)}$
= $\sqrt{(1-\frac{1}{\sqrt{2}})}\sqrt{(1+\frac{1}{\sqrt{2}})}$
= $\frac{1}{\sqrt{2}}$
= cosA