prove that: cot8a + cosec4a = cot2a - cosec8a
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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
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