Question

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

Answer 1

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

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

Answer 2

Answer:

We have,

sin (45° + θ) – cos (45°–θ)

= sin (45° + θ) - sin (90° -(45° - θ))

= sin (45° + θ) - sin (45° + θ)

= 0.

I hope this answer are helpful for your mate. Thanks!