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प्रश्न
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
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उत्तर
`sec theta = "ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 13/5`
Now consider a right-angled Δle ABC
By applying Pythagoras theorem
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
169 = 𝑥2 + 25
𝑥2 = 169 − 25 = 144
𝑥 = 12
`cos theta = 1/sec theta = (1/13)/5 = 5/13`
`tan theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 12/5`
`sin theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 12/13`
`cosect theta = 1/sin theta = 1/(12/13) = 13/12`
`sec theta = 1/cos theta = 1/(5/13) = 13/5`
`cot theta = 1/tan theta = 1/(12/5) = 5/12`
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