Math, asked by architamaharana333, 6 days ago

5 tan theta = 4, find cot theta and cosec theta​

Answers

Answered by aashutosh72
1

Answer:

Given5tanθ=4

or

cosθ

sinθ

=

5

4

∴sinθ=

5

4

cosθ

Thegiventrigonometricexpressionis→

5sinθ+2cosθ

5sinθ−3cosθ

(Substitutingsinθ=

5

4

cosθ)

=

5

4

cosθ+2cosθ

5

4

cosθ−3cosθ

=

4+2

4−3

=

6

1

Answered by diwanamrmznu
3

\huge\star\pink{solution}

let's →∅theta =a

 =  > 5 \tan(a) = 4 \\  \\  =  >  \tan(a) =  \frac{4}{5}   =  \frac{parpandicular(p)}{base(b)}  \\  \\paythagoras \: property \\  \\ =  >  h {}^{}  =  \sqrt{p {}^{2} + b {}^{2}  }  \\  \\ h =  \sqrt{4 {}^{2} + 5 {}^{2}  }  \\  \\  =  > h  =  \sqrt{16 + 25}  \\  \\   =  > h =  \sqrt{41}  \\  \\ to \\  \cot(a)  =  \frac{b}{p}  =  \frac{5}{4}  \\  \\ and \:  \cosec(a) =  \frac{h}{p}  =  \frac{ \sqrt{41} }{4}

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relative to trigonometry

 =  >   \sin(a)  =  \frac{1}{ \cosec(a) }  \\  \\  =  >  \cos(a)  =  \frac{1}{ \sec(a) }  \\  \\  =  >  \tan(a)   =  \frac{1}{ \cot(a) } \\  \\  =  >  \sin {}^{2} (a) +  \cos {}^{2} (a)   = 1 \\  \\  =  > 1 +  \tan {}^{2} (a)    =  \sec {}^{2} (a)  \\  \\  =  > 1 +  \cot {}^{2} (a)  =  \cosec {}^{2} (a)

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I hope it helps you

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