How do you find sec 2x, given tan x = 5/3 and sin x< 0?
Starting from tan x, you can find sec x, because of the trigonometric identity 1 +
But since x is in Quadrant II, sec x has to be negative. That's because sec x has the same sign as cos x, because sec x = 1 / cos x. We know that cos x is negative is Quadrant II, therefore so is sec x. So,
Since sec x and cos x are reciprocals of each other,
cos x = 1/sec x = -
Now use the identity
Again, we know that sin x is positive in Quadrant II
substituting the values,