Question

65
If 3 sin x + 5 cos x = 5 find the value of (3 cos x - 5 sin
n x)
is​

Answer 1

Answer:

+/- 3

Step-by-step explanation:

3 sin x + 5 cos x =5

squaring on both sides

(3 sinx +5 cos x )^2= 25

9 sinx ^2 x+ 25 cos^2 x+ 30 sinx cosx =25 ....equation 1

similarly

3cosx -5sinx = k

s.o.b.s

9 cos^2x + 25 sin^2 x - 30 sinx cosx = k^2....equation 2

add eqn1 and eqn2

9sin ^2x + 25 cos ^2 x +30 sinx cos x=25

+ 25 sin^2x 9 cos ^2 x - 30 sin x cos x =k^2

_____________________________________

34 sin ^2 x + 34 cos ^2 x = 25 + k^2

34 = 25 +k^2

k = +/- 3