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Simplify the given expression: sec ²t csct csc²t sect

Simplify the given expression: sec ²t csct csc²t sect. Simplify the giving expression: (sinx + cosx)(sinx – cosx) + 1 sin ²x. Prove the identity: Sin t = 1 + cost 1-cost sint. Prove the identity: (sinx + cosx) ² - sin2x = 1. Prove the identity:

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Simplify the given expression: sec ²t csct csc²t sect

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  1. Simplify the given expression: sec²t csct csc²t sect

  2. Simplify the giving expression: (sinx + cosx)(sinx – cosx) + 1 sin²x

  3. Prove the identity: Sin t = 1 + cost 1-cost sint

  4. Prove the identity: (sinx + cosx)² - sin2x = 1

  5. Prove the identity: tanx + cotx = secxcscx

  6. Prove the identity: (1-cos²x)cscx = sinx

  7. Prove the identity: 1 + secx = cscx tanx + sinx

  8. Using an addition or subtraction identity find the exact value of: Cos 7π/12

  9. Using an addition or subtraction identity, find the exact value of the following: Sinπ/12

  10. Rewrite the following in terms of sin x and cos x. (hint: use addition or subtraction identity) Sin (π/2 +x)

  11. Simplify the given expression: Cos(x+y) – cos(x-y)

  12. If x is in Q1 and y is in Q2, sinx = 24/25, and siny =4/5 find the exact value of sin(x+y) and tan(x+y).

  13. Use the half angle identities to solve the following: Cos 7π/8

  14. Use the half angle identities to solve: Tan 5π/8

  15. Write each as a sum or difference: cos2xcos4x

  16. Write each expression as a product: Sin9x – sin5x

  17. For the given, find the sin2x, cos2x, tan2x Cos x = -⅓ for π/2 < x < π

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