Question

prove that: cot8a + cosec4a = cot2a - cosec8a

Answer 1

Answer:

cot8a + cosec4a = cot2a - cosec8a

Step-by-step explanation:

prove that: cot8a + cosec4a = cot2a - cosec8a

LHS = Cot8a + Cosec4a

= Cos8a/Sin8a + 1/Sin4a

= Cos8a/ 2Sin4aCos4a + 1/Sin4a

= (Cos8a + 2Cos4a)/(2Sin4aCos4a)

= (Cos8a + 2Cos4a)/Sin8a

=(2Cos^2(4a) - 1 + 2Cos4a)/Sin8a

= (2Cos4a(Cos4a + 1) - 1)/Sin8a

= (2Cos4a(2Cos^2(2a) -1)/Sin8a

=(4 Cos^2(2a)Cos4a -1)/Sin8a

rhs

cot2a - Cosec8a

= Cos2a/ Sin2a - 1/Sin8a

= Cos2a/Sin2a - 1/2Sin4aCos4a

=Cos2a/ Sin2a - 1/4Sin2aCos2aCos4a

= (Cos2a(4Cos2aCos4a) - 1)/Sin8a

= (4Cos^2(2a)Cos4a - 1)/Sin8a

LHS = RHS