Question

if cos theta + sin theta is equal to root 2 cos theta show that cos theta minus sin theta is equal to root 2 Sin Theta​

Answer 1

$\huge\mathfrak{Answer}$

let theta = x

cos x + sin x = root2 cos x

squaring on both side, we get......

cos2x + sin2x + 2cosxsinx = 2cos2x

2sinxcosx = 2cos2x - cos2x - sin2x

2sinxcosx = cos2x - sin2x

2sinxcosx = (cosx+sinx) (cosx - sinx)

2sinxcosx = (root2 cosx) (cosx - sinx)

2sinxcosx/root2 cosx = cosx - sinx

root2 sinx = cosx - sinx

Answer 2

Answer:

Step-by-step explanation:

CosA + sin A = /2cosA

SinA = /2cosA -cos A

= cosA ( /2-1) × (/2+1) ÷ (/2+1)

= cosA÷/2+1

SinA(/2+1)=cos A

To prove = cosA - SinA= /2 sinA

Putting value of cos A

SinA (/2+1)-sinA

/2 sinA + sinA- sinA

=/2sin A

Hence proved

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