Question

if sinø = 4/5,find the value of 4sinø-cosø by 4 sinø+ cosø​

Answer 1

Step-by-step explanation:

Given  :-  sin ∅ = 4/5

We know that  [ sin²∅ + cos²∅ = 1 ]

∴ (4/5)² + cos²∅  = 1

∴ (16 / 25) + cos²∅ = 1

∴ cos²∅ = 1 - ( 16 / 25)

∴ cos²∅ = (9 / 25)

∴ cos ∅  = √ (9 / 25)

∴ cos ∅  = (3 / 5)

Now we know the values of sin ∅ and cos ∅

∴ (4 sin ∅ - cos ∅) / ( 4 sin ∅ + cos ∅)

= ( 4( 4/5 ) - ( 3/5 )  /  ( 4( 4/5 ) + ( 3/5 )

= ( ( 16/5 ) - ( 3/5 ) )  /  ( ( 16/5 ) + ( 3/5 ) )

= ( 13/5 ) / ( 19/5 )

= ( 13 / 19 )

∴ Answer =  ( 13/19 )

I Hope the Answer Helps !!!