Q. 34.3( 3 Votes )

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

Answer :

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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