The exact value of cos 105° is equals to √2/4 - √6/4.
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
In this case, 105 degrees, can be split into 45+60 (cos (45+60))
Use the sum formula for cosine to simplify the expression;
cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).
The exact value of cos(60) is 1/2.
So, multiply 1/2 to cos (45) - sin (60) times sin (45).
The exact value of cos (45) is the square root of 2 over 2
(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)
The Value of sin (60) is √3/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)
The exact value of sin (45) is √2/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2
Therefore, The exact value of cos 105° is equals to √2/4 - √6/4.
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