Question

then find the value


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Answer 1

after doi g this u hv to rationalise it

Answer 2

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\underline{\mathfrak{\orange{\bf{Given}}}}}}$

• sin θ = 3/4 ,

$\Large{\underline{\underline{\mathfrak{\orange{\bf{Find}}}}}}$

• Value of (tan θ . cosec θ - 1 )

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

We Know,

★ cosec θ = Hypotenuse/Perpendicular

★ tan θ = Perpendicular/Base

★ sin θ = Perpendicular/Hypotenuse

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In Diagram,

• AB = perpendicular = 3
• BC = Base
• CA = Hypotenuse = 4.

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Now, in right ∆ABC

Pythagoras's Theorem

★ (Hypotenuse)² = (perpendicular)² + (Base)²

So Now,

➥ Base² = (Hypotenuse)² - (perpendicular)²

➥ BC² = 4² - 3²

➥ BC² = 16 - 9

➥ BC² = 7

➥ BC = √7

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So Now calculate tan θ.

➥ tan θ = Perpendicular/Base = AB/BC

➥ tan θ = 3/√7

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Now Calculate cosec θ,

➥cosec θ = Hypotenuse/Perpendicular = CA/AB

➥ cosec θ = 4/3

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Now, Calculate ,

➥ (tan θ . cosec θ - 1 )

Keep all above values,

➥ ( 3/√7) × ( 4/3) - 1

➥ 4/√7 - 1

➥ (4 - √7)/√7 Ans.

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$\Large{\underline{\underline{\mathfrak{\red{\bf{Hence}}}}}}$

• Value of (tan θ . cosec θ - 1 ) will be = (4 - √7)/√7.

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