Question

Cos square 25 + cos square 95 + cos square 145 =?

Answer 1

Cos²25°  + Cos²95°  + cos²145° = 3/2

Step-by-step explanation:

Cos²25°  + Cos²95°  + cos²145°

using Cos²A  + Cos²B =  1 + Cos(A+B)Cos(A - B)

=   1  + Cos(95° + 25°)Cos(95° - 25°) + cos²145°

= 1 + Cos(120°)Cos(70°) + cos²145°

= 1   -  (1/2)  Cos(70°) + Cos²145°

= 1  + (1/2) ( 2Cos²145° - Cos(70°))

=  1  + (1/2) ( 2Cos²35° - Cos(70°))

2Cos²α  = Cos2α  + 1

= 1   + (1/2)( Cos70° + 1 - Cos70° )

= 1 + (1/2)(1)

= 1 + 1/2

= 3/2

Cos²25°  + Cos²95°  + cos²145° = 3/2

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Answer 2

Answer:

I hope this is the required solution