4 Simplify each expression a 1 sin oc1 sin oc b cscxtan x se

4. Simplify each expression. a. (1 sin oc)(1 sin oc) b. cscxtan x sec(+x) 1 sin (+x) 1+sinox COS OX

Solution

a. (1-sin alpha)(1+sin alpha) = 1-sin²alpha = cos²alpha

b. cscx tan x + sec x = sec x + sec x= 2sec x

c. 1/(1+sin alpha) + sin alpha/cos²alpha = (cos²alpha +sin alpha +sin²alpha)/((1 +sin alpha)cos²alpha)

                                                         = (1+sin alpha)/(1+sin alpha)cos²alpha)=1/cos²alpha =sec²alpha