Question
Use identities to find the exact value of the trigonometric expression below.
1/cos2 * π/16 - 1/cot2 * π/16
PS: in words, the problem is, one divided by cosine-squared, then beside the cosine-square (still in the denominator) is pi/16. Minus one divided by cotangent-squared, then beside the cotangent-squared (still in the denominator) is pi dived by 16.) please show steps so that I can learn this.
1/cos2 * π/16 - 1/cot2 * π/16
PS: in words, the problem is, one divided by cosine-squared, then beside the cosine-square (still in the denominator) is pi/16. Minus one divided by cotangent-squared, then beside the cotangent-squared (still in the denominator) is pi dived by 16.) please show steps so that I can learn this.
Answers
Reiny
let x = π/6 for easier typying
so your 1/cos2 * π/16 - 1/cot2 * π/16
= 1/cos^2 x - 1/cot^2 x
= sec^2 x - tan^2 x
since sec^2 x = 1 + tan^2 x ,
= 1 + tan^2 x - tan^2 x
= 1
so your 1/cos2 * π/16 - 1/cot2 * π/16
= 1/cos^2 x - 1/cot^2 x
= sec^2 x - tan^2 x
since sec^2 x = 1 + tan^2 x ,
= 1 + tan^2 x - tan^2 x
= 1