Question

if tanA=24/7 then prove that sinA-COSA/sinA+COSA=17/31​

Answer 1

Step-by-step explanation:

as TanA= Perpendicular/Base

therefore in a triangle where perpendicular is 24x and base is 7x, Hence by Pythagoras theorem, Hypotenuse=25x.

therefore, SinA=24/25 and CosA=7/25

so, SinA-CosA=17/25 (consider it as eq.1)

and SinA+CosA=31/25 (consider it as eq.2)

therefore, eq1/eq2= 17/31

Answer 2

Answer:

Step-by-step explanation:

Given that,

tanA = 24/7 = AB/ BC ( ∵In right angle triangle ABC )

By using Pythagoras theorem,

AC² = AB² + BC²

AC² = ( 24 )² + ( 7 )²

AC² = 576 + 49

AC² = 625

AC = √625

AC = 25

sin A = AB / AC = 24/25,

cos A = BC / AC = 7/25.

∴ L.H.S. = sin A - cos A / sin A + cos A

= ( 24/25 - 7/25 ) / ( 24/25 + 7/25)

= ( 24 - 7 / 25 ) / ( 24 + 7 / 25 )

= ( 17 / 25 ) / ( 31 / 25 )

= 17/25 × 25/31

= 17/31

= R.H.S.

∴L.H.S. = R.H.S.

Hence, it is proved.