Question

If 3cot teta =4,find the value of 5sin teta -3 cos teta/5 sin teta +3 cos teta

Answer 1

Theta is written as A , please ignore A with ^ , its due to little mistake in writing.

Given, 3 cot A = 4

Or, cot A = 4 / 3

$\frac{base}{height} = \frac{4}{3} \:\:\:\:\:\:\: | \: \: cot A = \frac{base }{ height }$

Then,Let base = 4x and height = 3x

By Pythagoras theorem,

( 4x )^2 + ( 3x )^2 = ( hypotenuse )^2

25 x ^2 = hypotenuse^2

5x = hypotenuse

So,

sin A = $\frac{ height }{ hypotenuse }$

sin A = $\frac{3x}{5x } = \frac{ 3 }{ 5 }$

5 sin A = 5 × $\frac{3}{5}$

5 sin A = 3    ---------: ( 1 )

And, cos A = $\frac{base }{ hypotenuse }$

cos A = $\frac{4x}{5x} = \frac{4}{5}$

3 cos A = 3 × $\frac{4}{5}$

3 cos A = $\frac{12}{5}$     -------: ( 2 )

Now,

5 sin A + 3 cos A  [ Put values from ( i ) and ( ii )  ]

→3 + $\frac{12}{5}$

→ $\frac{27}{5}$     ---------: ( 3 )

5 sin A - 3 cos A

3 - $\frac{12}{5 }$

$\frac{3}{5}$   ------: ( 4 )

Hence,

$\frac{ 5 sin A - 3 cos A }{ 5 sin A + 3 cos A }$

Putting values from ( 3 ) and ( 4 ) ,

→ $\frac{\frac{3}{5}}{\frac{27}{5} }$

⇒ $\frac{1}{9}$

Answer 2

$\huge\color{lightblue}\boxed{\mathbb{A}nswer:}$






$\bold{Refer\:to\:the\:attachment\:above\:for\:your\:solution}$






$\huge\boxed{Thanks!!!}$







$\huge\underline\red{\bold{Hope\:it\:helps!!!}}$