Question

cos square 25+ cos square 95+ cos cube145

Answer 1

⇒cos 95º+cos 25º = 2 cos1/2}(95^o+25^o)xcos\frac{1}{2}(95^o-25^o)cos 95o+cos 25o=2.cos21​⇒(95o+25o).cos21​(95o−25o)

⇒cos~95^o+cos~25^o = 2.cos\frac{1}{2}(120^o).cos\frac{1}{2}⇒(70^o)cos 95o+cos 25o=2.cos21​(120o).cos21​(70o)

⇒cos 95° + cos 25° = 2 cos 60°. cos 35°

⇒Ingat, cos 60° = ¹/₂

⇒cos~95^o+cos~25^o = 2.\frac{1}{2}.cos~35^ocos 95o+cos 25o=2.21​.cos 35o

⇒\boxed{cos~95^o + cos~25^o = cos~35^o}cos 95o+cos 25o=cos 35o​

\boxed{Step-2:cos~95^o+cos~25^o+cos~145^o}Step−2:cos 95o+cos 25o+cos 145o​



⇒cos~145^o+cos~35^o = 2.cos\frac{1}{2}(145^o+35^o).cos\frac{1}{2}(145^o-35^o)cos 145o+cos 35o=2.cos21​⇒(145o+35o).cos21​(145o−35o)

⇒cos~145^o+cos~35^o = 2.cos\frac{1}{2}(180^o).cos\frac{1}{2}(110^o)cos 145o+cos 35o=2.cos21​(180o).cos21​(110o)

⇒cos 145° + cos 35° = 2 cos 90°. cos 110°

⇒Ingat, nilai cos 90° = 0, sehingga

⇒cos 145° + cos 35° = 2. 0. cos 110°

⇒cos 145° + cos 35° = 0

Answer 2

Cos²25°  + Cos²95°  + cos²145° = 3/2

Step-by-step explanation:

correct Question is :

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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