Question

(cot A * cot 4A + 1)/(cot A * cot 4A - 1) = (cos 3A)/(cos 5A)

Answer 1

Step-by-step explanation:

L.H.S = cotA cot4A + 1/cotA cot4A - 1

= cosA/sinA * cos4A/sin4A + sin4A/Sin4A * sinA/SinA / cosA/sinA * cos4A/sin4A-sin4A/Sin4A * sin4A/sin4A

= CosA cos4A+sin4A sinA/sinA sin4A/

CosA cos4A-sin4A sinA/SinA Sin4A

= CosA cos4A + sin4A sinA/CosA cos4A - sin4A sinA

Now,we know CosA CosB + sinB sinA= Cos(A-B) and

CosA Cos4A - Sin4A SinA = Cos(A+B)

So,

= Cos(A-4A)/Cos(A+4A) we know, cos(-x) =cos x

= Cos(3A)/Cos(5A)

= R.H.S