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If 8tanA = 15, find sinA - cosA. - Mathematics

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Sum

If 8tanA = 15, find sinA - cosA.

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Solution

8tanA = 15

⇒ tanA = `(15)/(8) = "Perpendicular"/"Base"`

Hypotenuse
= `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((15)^2 + (8)2`
= `sqrt(225 + 64)`
= `sqrt(289)`
= 17
sinA - cosA = `"Perpendicular"/"Hypotenuse" - "Base"/"Hypotenuse"`

= `(15)/(17) - (8)/(17)`

= `(15 - 8)/(17)`

sinA - cosA = `(7)/(17)`.

Concept: Reciprocal Relations
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APPEARS IN

Frank Class 9 Maths ICSE
Chapter 26 Trigonometrical Ratios
Exercise 26.1 | Q 24
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