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sulaksh asked this question on Class X » Math » Introduction to Trigonometry

IF 5Sinx + 3Cosx = 4, Find value of  3Sinx - 5Cosx where x is theta.

Asked by sulaksh(student), on 10/3/10
Answers

It's simple.Look at the solution -----

By the 1st equation find the value sinx now put it equal to perpendicular (P) / hypotenuse (H) and to get actual values of P and H multiply both by some positive integer let K.Now by Pythagoras Theorem find B (Base) and now find cosx by B / H. Now,put the values of sinx and and cosx in the second equation.You will get the answer.

Thanks and Best of Luck of the exams

Posted by NITIN(student), on 10/3/10

 could you solve it?

Posted by gull0210(student), on 10/3/10

Let ... 3 sin x + 5 cos x = 5.

∴ ( 3 sin x + 5 cos x )² = 5²

∴ 9 sin² x + 25 cos² x + 30 sin x cos x = 25

∴ 9(1-cos² x) + 25(1-sin² x) + 30 sin x cos x = 25

∴ 9 - 9cos² x + 25 - 25sin² x + 30 sin x cos x = 25

∴ 9 = 25 sin² x + 9 cos² x - 30 sin x cos x

∴ 9 = ( 5 sin x - 3 cos x )²

∴ 5 sin x - 3 cos x = ± √9

∴ 5 sin x - 3 cos x = ± 3 .............

THNX AND THUMZ UP PLS

Posted by verma.sangam(student), on 10/3/10
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