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Question
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
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Solution
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
⇒ `sin(90^circ - 18^circ)/cos18^circ - sec(90^circ - 58^circ)/(cosec58^circ)`
⇒ `cos18^circ/cos18^circ - (cosec 58^circ)/(cosec58^circ) = 1 - 1 = 0`
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RELATED QUESTIONS
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Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
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If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
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∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
