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If 15 Cot a = 8 Find All the Values of Sin a and Sec a - Mathematics

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If 15 cot A = 8 find all the values of sin A and sec A

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Solution

We have,
15 cot 𝐴 = 8
⟹ cot 𝐴 =`8/15`
As,
`cosec^2 A = 1 + cot^2 A`

  =`1+(8/15)^2`

= `1 + 64/225`

= `(225+64)/225`

`⇒ cosec^2A=289/225`

`⇒ cosec A = sqrt(289/225)`

`⇒ cosec A = 17/15`

`1/sin A = 17/15`

`sin A = 15/17`

Also,

`Cos^2 A = 1-sin^2 A`

`= 1- (15/17)^2`

`= 1-225/289`

`=(289-225)/289`

`⇒ cos^2 A = 64/289`

`⇒ cos A = sqrt(64/289)`

`⇒ cos A = 8/17`

`⇒ 1/sec A = 8/17`

`⇒ sec A = 17/8`

 

Concept: Trigonometric Ratios and Its Reciprocal
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 5 Trigonometric Ratios
Q 7
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