1. what is the value of x? sin(x+22)°=cos(2x−7)° 2.given cosx=1213 and sinx=513 . what is ratio for tanx ? leave answer as a fraction in simplest form

 the  sine and cosine  are co-functions

So

sin (theta) = cos (90 - theta)> This implies that  the angles sum to 90°

therefore

( x + 22)  + (2x - 7)  =  90    simplify

3x + 15  = 90     subtract  15 from both sides

3x  =  75      divide both sides by 3

x  = 25

 The answer Part 1) is x=25°

 Part 2) Given cos x=12/13 and sin x =5/13

What is ratio for  tanx  ?

 we know that

tan x = sinx / cos x

tan x  =   (5/13) / (12/13)   =  (5/13) * (13/12)  =  5/12

the answer Part 2) is 5/12