Find the numerical value of csc^2(x)

Question

6 sin^2(x) - 7 cos^2(x) = 1 

 

Find the numerical value of
csc^2(x)

Answer 1

6sin²x - 7cos²x = 1

 

   Recall that sin²x + cos²x = 1.  So, cos²x = 1 - sin²x.

 

The original equation can then be rewritten as:                                       6sin²x - 7(1-sin²x) = 1

 

                   13sin²x = 8

 

                      sin²x = 8/13

 

                 So, csc²x = 1/sin²x = 13/8