Question

Trignometry Challenge (15 points ) -
If , sinQ + cosQ=1
Then Prove , 2sinQ -cosQ =2

Answer 1

sinQ+ cosQ=1
root2 {1/root2. sinQ+1/root2.cosQ}=1
root2 {cos45.sinQ +cosQ.sin45}=1
sin (Q+45)=1/root2
sin (Q+45)=sin45

solve by trigeometric general solution.

Q+pi/4=n.pi +(-1)^n (pi/4)

put n=0
Q+ pi/4=0 +pi/4 , Q=0,

put n=1
Q+ pi/4=pi -pi/4
Q=pi/2
=========
=======
here we see Q=0, pi/2 ......
but condition
here proving 2sinQ-cosQ=2
so,
we only use Q=pi/2 not Q=0

now 2sinQ-cosQ=2 only when Q=pi/2

Answer 2

Answer:

I don't know sorryyyyyyyy