sum and difference identities for cosine?

Question

Find the exact functional value using the cosine sum or difference identity.

sec (-pi/12)

Answer 1

sec(-pi/12) = 1/cos(-pi/12) = 1/cos(pi/12).

cos(pi/6) = sqrt(3)/2 = cos(2 pi/12)= cos^2(pi/12) - sin^2(pi/12) = 2 cos^2(pi/12) - 1. Hence,

cos^2(pi/12) = (1 + sqrt(3)/2)/2. Since pi/12 is in the first quadrant, its cosine is positive, so that

cos(pi/12) = sqrt((1 + sqrt(3)/2)/2). Finally,

sec(-pi/12) = sec(pi/12) = 1/(sqrt((1 + sqrt(3)/2)/2))

Answer 2

cos(-a) =cos a and sin(-a)= -sina so the above problem turns into cos10'cos35'-sin10'sin35' cosacosb-sinasinb= cos(a+b) formula so cos(10+35) = cos45 =a million/sqrt(2) for this reason the soln