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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