Question

sin 65+cos 65=√2 cos 20

Answer 1

Answer :

Now,

cos20

= cos (65 - 45)

= cos65 cos45 + sin65 sin45

= cos65 (1/√2) + sin65 (1/√2)

=> cos65 + sin65 = √2 cos20

=> sin65 + cos65 = √2 cos20

Hence, proved.

We used the identity rule -

cos (A - B) = cosA cosB + sinA sinB

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Answer 2

Answer:

$cos(25) + \cos(65) = \sqrt{2} \cos(20)$