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प्रश्न
In the given figure, if sin θ = `7/13`, which angle will be θ?
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उत्तर
Given: sin θ = `7/13`
According to the trigonometric ratios formula,
sin θ = `"Perpendicular"/"Hypotenuse"`
= `7/13`
Hence, the angle θ is ∠XZY.
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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` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
