How do evaluate (1/cos^2 40) - (1/cot^2 40)? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer maganbhai P. Apr 25, 2018 #1# Explanation: We know that, #color(blue)((1)1/cos^2theta=sec^2theta and 1/cot^2theta=tan^2theta# #color(red)((2)sec^2theta-tan^2theta=1# Let, #X=1/cos^2 40-1/cot^2 40...tocolor(blue)(Apply(1))# #X=sec^2 40-tan^2 40...tocolor(red)(Apply(2)# #X=1# Answer link Related questions How do you find the trigonometric functions of any angle? What is the reference angle? How do you use the ordered pairs on a unit circle to evaluate a trigonometric function of any angle? What is the reference angle for #140^\circ#? How do you find the value of #cot 300^@#? What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#? How do you know if #sin 30 = sin 150#? How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle Impact of this question 2895 views around the world You can reuse this answer Creative Commons License