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рдкреНрд░рд╢реНрди
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan alpha = 5/12`
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рдЙрддреНрддрд░
`tan alpha = 5/12`
We know that `tan alpha ="opposite side/adjacent side"= 5/12`
Now consider a right-angled Δle ABC
Let x = hypotenuse .By applying Pythagoras theorem
ЁЭР┤ЁЭР╢2 = ЁЭР┤ЁЭР╡2 + ЁЭР╡ЁЭР╢2
ЁЭСе2 = 52 + 122
ЁЭСе2 = 25 + 144 = 169
ЁЭСе = 13
`sin α = "adjacent side"/"hypotenuse"= 5/13`
`cos α = "adjacent side"/"hypotenuse" = 12/13`
cot α = `1/tan alpha = 12/15``
cosec α = `1/sin alpha = (1/5)/13 = 13/5`
sec α = `1/cos alpha = (1/12)/13 = 13/12`
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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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