Question

please solve this for me

Answer 1

Hi ,

LHS = cos⁴ A - sin⁴ A + 1

= ( cos² A )² - ( sin² A )² + 1

= ( Cos² A + sin² A)(cos²A - sin² A ) + 1

= cos² A - sin² A + 1

= cos² A - ( 1 - cos² A) + 1

= cos² A - 1 + cos² A + 1

= 2cos² A

= RHS

I hope this helps you.

: )

Answer 2

cos^4A - sin^4 A + 1
= (cos^2A)^2 - (sin^2A)^2 + 1
Using identity a^2 - b^2 = (a+b)(a-b)
= (cos^2A + sin^2A)(cos^2A - sin^2A) + 1
Now by identity sin^2A + cos^2A = 1
= 1 * (cos^2A - sin^2A) + 1
= cos^2A + 1 - sin^2A
= cos^2A + cos^2A (using identity sin^2A + cos^2A = 1)
= 2cos^2A
= RHS.

Hence proved.