SOLUTION: If sec(a+15)=csc(2a) , find the smallest positive value of a, in degrees? I kind of know how to start it but i dont understand what a means?

Cross-multiply





We need to get that difference to a product.  One well-known
difference to product formula is



We can use it if we can write sin(2a) as a cosine.  We can
do that by using the cofunction identity, and write sin(2a) = cos(90°-2a)





Use the identity with x = 90°-2a and y = a+15°

  


  

  

Divide both sides by -2

  

Use the zero-factor property:

      and        


      and       

Multiply both equations through by 2

105°-a = 360°n             and       75²-3a = 360°n
      -a = 360°n-105°                   -3a = 360°n-75°
       a = -360°n+105°                    a = -120°n+25°

Both have their smallest positive value when n=0

       a = -360°(0)+105°                  a = -120°(0)+25°
       a = 105°                           a = 25°

So the smallest positive value of a is 25°

Edwin