Please help me solve this - PreCalc

posted by chizoba

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. 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

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