Question

if 3sin+5cos=4 then number of integer value of expression (5sin-3coos) takes place are

Answer 1

Answer:

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

Step-by-step explanation:

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