Key Idea: This topic links all six trig functions. You simplify expressions and prove identities by hand on Paper 1.
Relationships between trig functions
- sec = 1/cos, csc = 1/sin, cot = cos/sin.
- 1 + tan² = sec² and 1 + cot² = csc², both from sin² + cos² = 1.
Proving an identity
- One side — Work on one side only until it matches the other.
- Stuck? — Rewrite everything in sin and cos.
- Combine — Use a common denominator, then sin² + cos² = 1.
Never move terms across the = sign in a proof.
Simplify (sec²θ − 1)/sec²θ. sin²θ.
Which identity turns sec²θ − 1 into tan²θ? 1 + tan²θ = sec²θ.
How do you get 1 + cot² = csc²? Divide sin² + cos² = 1 by sin².
What is cot in terms of sin and cos? cos/sin.