Complete the identity 25 csc x cot x secx A sec2 x B 1 26

Complete the identity 25) csc x cot x = ? secx A) sec2 x B) 1 26) tan x(cot x-cos x) = ? A) 0 B) 1 27) sin x + cos x = ? cos x sin x A) 1+cotx B) -2 tan2 Find the exact value of the expression. 28) cos (165°) cos (45°)+sin (165°) sin (45 A) -N3 B) 2 Complete the identity. 29) cos (x ) = ?

Solution

25) (csc x *cot x)/sec x = (1/sin x *cos x/sin x)/(1/cos x) = (cos²x/sin²x) = cot²x

26) tan x*(cot x – cos x) = tanx*cotx – tanx*cosx = tanx(1/tanx) – (sinx/cosx)*cosx = 1 – sinx

27) (sinx/cosx) + (cosx/sinx) = (sin²x + cos²x)/(sinx*cosx) = 1/(sinx*cosx)