Question

given cot theta is equal to 20 divided by 21 determine cos theta and Cosec
theta​

Answer 1

Answer :

• cosec θ = 29 / 21
• cos θ = 20 / 29

Given :

• cot θ = 20 / 21

To find :

• cos θ = ?
• cosec θ = ?

Solution :

Using trigonometric identity

→ 1 + cot²θ = cosec²θ

→ cosec²θ = 1 + ( 20/ 21 )²

→ cosec²θ = 1 + ( 400 / 441 )

→ cosec²θ = ( 441 + 400 ) / 441

→ cosec²θ = 841 / 441

→ cosec θ = √( 841 / 441 )

→ cosec θ = 29 / 21

Hence,

• cosec θ is equal to 29 / 21

Now since, cosec θ = 1 / sin θ

therefore,

→ sin θ = 21 / 29

squaring both sides

→ sin²θ = 441 / 841

using trigonometric identity

→ 1 - cos²θ = 441 / 841

→ cos²θ = 1 - ( 441 / 841 )

→ cos²θ = ( 841 - 441 ) / 841

→ cos²θ = 400 / 841

→ cos θ = √ ( 400 / 841 )

→ cos θ = 20 / 29

Hence,

• cos θ is equal to 20 / 29

Answer 2

$\star\:\:\:\bf\large\underline\blue{Given:—}$

$Cot∅=\frac{20}{21}$

$\star\:\:\:\bf\large\underline\blue{To\:find:—}$

• Cos∅ = ?
• Cosec∅ = ?

$\star\:\:\:\bf\large\underline\blue{Solution:—}$

$cosec∅ = \sqrt{1 + ( \frac{20}{21} )^{2} } \\ = \sqrt{1 + \frac{400}{441 } } \\ = \sqrt{ \frac{841}{441} } \\ = \frac{29}{21}$

As , Sin∅ =1/cosec∅

Therefore, Sin∅ = 21/29

Now,

$cos∅ = \sqrt{1 - ( \frac{21}{29})^{2} } \\ = \sqrt{1 - \frac{441}{841} } \\ = \sqrt{ \frac{400}{841} } \\ = \frac{20}{29}$

Therefore, cos∅ = 20/29

and cosec∅ = 29/21

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