Question

If 3 cot theta equals to 4 find the value of 5 sin theta minus 3 cos theta upon 5 sin theta + 3 cos theta

Answer 1

Hi ,

Here I'm using A instead of theta

CotA= 4/3-----( 1 )

Now ,

(5sinA + 3cosA )/(5sinA - 3cosA )

Divide numerator and denominator with sinA , we get

= ( 5 + 3cosA/sinA)/(5 - 3cosA/sinA)

= ( 5 + 3cotA) / ( 5 - 3cotA )

= ( 5 + 3 ×4/3 )/ [ 5 - 3× ( 4/3 ) ]

= ( 5 + 4 ) / ( 5 - 4 )

= 9/1

= 9

I hope this helps you.

:)

Answer 2

Answer

Given, 3cotθ=4

∴cotθ=  4/3 = B/P

USING PYTHAGORAS THEOREM.,

H² = B² + P²

H² = 4² + 3²

H² = 16+9

H² = 25

H = $\sqrt{25}$ = 5

Now,  

5sinθ-3cosθ = (5 X 3/5) - (3 X 4/5)

= 15/5 - 12/5

= 3/5

5sinθ+3cosθ = (5 X 3/5) + (3 X 4/5)

= 15/5 + 12/5

= 27/5

THEREFORE , 5sinθ−3cosθ/5sinθ+3cosθ

3/5/27/5

5 GETTING CANCELLED

= 3/27 = 1/9

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