(sina-cosa)^2=1-sin2a

Open in App

Solution

(sina-cosa)^2=1-sin2a

LHS (a-b)^2 = a^2 + b^2 - 2ab
(sin a - cos a)^2 = sin^2 a + cos^2a - 2 cos a sin a [ identity: sin^2 a + cos^2a =1]
(sin a - cos a)^2 = 1 - 2 cos a sin a [ sina = 2 sinA cosA]
= 1 - sin2A

Suggest Corrections

Similar questions

\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{s i n^{2} A - c o s^{2} A} = \frac{2}{2 s i n^{2} A - 1} = \frac{2}{1 - 2 c o s^{2} A}

\frac{sin 2 A}{sin A} - \frac{cos 2 A}{cos A} = sec A

\frac{cos A}{1 - tan A} - \frac{{sin}^{2} A}{cos A - sin A} = sin A + cos A

\frac{1 + sin 2 A}{cos 2 A} = \frac{cos A + sin A}{cos A - sin A} = cot (\frac{π}{4} - A)

sin A + cos A = 1

sin 2 A =

Join BYJU'S Learning Program