Question

Prove that :
Cos(45+A) cos(45-A) =1/2cos2A

Answer 1

Step-by-step explanation:

LHS

cos(45+A)cos(45-A)

(cos45cosA-sin45sinA)(cos45cosA+sin45sinA)

$( \frac{1}{ \sqrt{2} } cosa - \frac{1}{ \sqrt{2} } sina)( \frac{1}{ \sqrt{2} } cosa + \frac{1}{ \sqrt{2} } sina) \\ ( \frac{1}{ \sqrt{2} } cosa) {}^{2} - ( \frac{1}{ \sqrt{2} } sina) {}^{2} \\ \frac{cos {}^{2} a}{2} - \frac{si n{}^{2} a}{2} \\ \frac{1}{2}( cos {}^{2} a - sin {a}^{2} ) \\ \frac{1}{2} cos2a \: \: \: \: \ \: = rhs \: \\ proved$