Question

5 sin x+4cos x=3,4sinx-5cos x=

Answer 1

Answer:

5sinx+4cosx=3

Squaring both sides

25sin

2

x+16cos

2

x+2∗5∗4sinxcosx=9⇒9sin

2

x+7+40sinxcosx=0

⇒9sin

2

x+7=−40sinxcosx

Now, 4sinx−5cosx=

(4sinx−5cosx)

2

=

16sin

2

x+25cos

2

x−40sinxcosx

=

16sin

2

x+25cos

2

x+9sin

2

x+7

=

25sin

2

x+25cos

2

x+7

=

25+7

=

32

=4 root 2