Question

prove that cos^2A-sin^2A=1-2sin^2A​

Answer 1

TO PROVE:

⇒Cos²A-Sin²A=1-2Sin²A

SOLUTION:

By taking L.H.S.

⇒ Cos²A-Sin²A....(1)

We have identity:-

⇒[ Sin²A+Cos²A=1]

⇒ Cos²A=1-Sin²A

Put this value of Cos²A in equation 1.

⇒ (1-Sin²A)-Sin²A

⇒ 1-Sin²A-Sin²A

⇒ 1-2Sin²A

L.H.S.=R.H.S.

Hence proved