If cos theta minus sin theta is equal to root 2 Sin Theta prove that cos theta + sin theta is equal to root 2 cos theta

Open in App

Solution

Cos A - SinA = √2sinA
Squaring, (CosA - SinA)² = Cos²A +Sin²A - 2cosAsinA
(√2sinA)²= 1 - 2cosAsinA
2cosAsinA = 1 - (√2sinA)²2cosAsinA = 1- 2sin²A = 1-sin²A - sin²A= cos²A - sin²A
Squaring (CosA + sinA)²= 1 + 2cosAsinA = 1 + cos²A - sin²A
= cos²A + cos²A = 2cos²A
Therefore, CosA+ sinA = √2cosA

Suggest Corrections

Similar questions

, the solution set of equation 4sin theta into cos theta - 2 cos theta minus 2 root 3 sin theta + root 3 is equal to zero in the interval 0 to 2 pie is

Q. If

x = \frac{2 \sin θ}{1 + \cos θ + \sin θ}

, then prove that

\frac{1 - \cos θ + \sin θ}{1 + \sin θ}

is also equal to x.

Q. If

s i n θ + c o s θ = a, c o s θ - s i n θ = b

, then

s i n θ (s i n θ - c o s θ) + s i n^{2} θ (s i n^{2} θ - c o s^{2} θ) + s i n^{3} θ (s i n^{3} θ - c o s^{3} θ) + . . . .

is equal to

Join BYJU'S Learning Program