Question

If 3sin 5cos 5,     prove that 5sin 3cos 3      .​

Answer 1

Answer:

Step-by-step explanation: mark as brainlist

3sin+5cos = 5

square both side

(3sin + 5cos)² = 5²

9sin²+ 25cos² + 30Sincos = 25

9sin² + 30sinCos = 25-25cos²

9sin² + 30SinCos = 25Sin²    ( as sin² + cos²=1  )

30SinCos = 16Sin²

30Cos = 16 Sin

15 Cos = 8 Sin

Cos = 8/15 Sin

Put this into 3Sin + 5Cos = 5

3 Sin + 5 (8/15)Sin = 5

3 Sin +( 8/3) Sin = 5

9 Sin + 8 Sin = 15

Sin = 15 / 17

Cos = (8 /15)Sin

Cos = (8/15)(15/17)

Cos = 8/17

Putting cos & sin vales in 5Sin-3cos

= 5(15/17)-3(8/17)

= 75/17 - 24/17

= 51/17

= 3