1.

The value of cos 20 + 2sin² 55 – √2 sin65 is

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Answer:

❀ʀᴇǫᴜɪʀᴇᴅ ᴀɴsᴡᴇʀ:

⟹COS(20°)+2.sin2(55o)−2–√SIN(65°)

Using 2.{ \sin }^{2}θ=1−cos(2θ)

⟹cos(20°)+1−cos(110°)−2–√sin(65°)

⟹cos(20°)+1+sin(20°)−2–√sin(65°)

⟹cos(20°)+1+sin(20°)−2–√sin(65°)

Using 65 = 45 + 20

Using sin(65)=sin(45).cos(20)+cos(45).sin(20)

⟹cos(20°)+1+sin(20°)−\sqrt{2}(sin(45°).cos(20°)+cos(45°).sin(20°))

⟹cos(20°)+1+sin(20°)−cos(20°)−sin(20°)

⟹1

\sf\blue{hope \: this \: helps \: you!! \: }


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