Question

prove sos 55degrees + cos 65 degrees + cos 175degrees = 0

Answer 1

Answer:

Step-by-step explanation:

Given :

To prove, Cos 55° + Cos65° - Cos 175° = 0

Solution :

LHS = Cos 55° + Cos65° - Cos 175°

= (Cos 55° + Cos65°) - Cos 175°

= Cos (60 - 5)° + Cos(60 + 5)° - Cos (180 - 5)°

= 2 Cos60°(Cos5°) - Cos 5°   [∵ Cos(A + B) + Cos(A - B) = 2Cos A CosB]

= 2 × $\frac{1}{2}$ ×Cos 5° - Cos 5°

= Cos5° - Cos 5°

= 0

= RHS

Hence, Proved,.