Math, asked by jerrin25, 11 months ago

if 5sin +3cos=4 find the value of 3sin-5cos​

Answers

Answered by RaviMKumar
6

Answer:

3√2

Step-by-step explanation:

5 sinx + 3 cosx = 4

=> (5 sinx + 3 cosx)² = 4²

=> 25sin²x + 9cos²x + 30 sinx.cosx = 16

=> 25sin²x + 9cos²x  =   16 - 30.sinx.cosx

consider,  (3 sinx-5cosx)²

=  9sin²x+25cos²x-30sinx.cosx

=  9(1-cos²x)+25(1-sin²x) - 30sinx.cosx

= 9-9cos²x + 25 - 25sin²x - 30.sinx.cosx

= 34 - ( 25sin²x+9cos²x) - 30.sinx.cosx

= 34 - [ 16 - 30.sinx.cosx ] - 30sinx.cosx

= 34 -16 + 30.sinx.cosx - 30.sinx.cosx

= 18

=> (3 sinx-5cosx)² = 18

=> √(3 sinx-5cosx)² = √18

                                = √9*2 = 3√2

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