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рдкреНрд░рд╢реНрди
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
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рдЙрддреНрддрд░
consider a right-angled Δle ABC, we get
Let x be the adjacent side.
By applying Pythagoras theorem
ЁЭР┤ЁЭР╢2 = ЁЭР┤ЁЭР╡2 + ЁЭР╡ЁЭР╢2
`(sqrt10)^2 = 1^2 + x^2`
x2 = 10 − 1 = 9
x = 3
`sin theta = 1/cosec theta = 1/sqrt10`
`cos theta = "adjacent"/"hypotenuse" = 3/sqrt10`
`tan theta = "opposite sides"/"adjacebt side" = 1/3`
`sec theta = 1/cos theta = sqrt10/3`
`cot theta = 1/tan theta = (1/1)/3 = 3`
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Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[тИ╡ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[тИ╡ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[тИ╡ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
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