# Express the following in terms of trigonometric ratios of angles having measure between 0 and 45:(1) sin85 + cosec85(2) cos89 + cosec87(3) sec81 + cosec54

cos(90–θ ) = sinθ

tan(90–θ ) = cotθ

sin(90–θ ) = cosθ

cot(90–θ ) = tanθ

cosec(90–θ ) = secθ

sec(90–θ) = cosecθ

(1) sin85 + cosec85

sin(90–5) + cosec(90–5)

= cos5 + sec5

(2) cos89 + cosec87

cos(90–1) + cosec(90–3)

= sin1 + sec3

(3) sec81 + cosec54

sec(90–9) + cosec(90–36)

= cosec9 + sec36

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