Question

Prove that:
sin^4A-cos^4A=sin^2A-1
​

Answer 1

It is easy.consider LHS

Sin^4A-Cos^4A

(Sin^2A+Cos^2A)(sin^2A-cos^2A)

(1)(sin^2-1-sin^2A)

(2sin^2-1)

=RHS

Answer 2

Correct question:-

$Cos^2 A - Sin^2 A = 2 Sin^2 A - 1$

Given :-

$Sin^4A - Cos^4 A$

To prove :-

$2Sin^2A - 1$

Proof:-

Here we use a Trigonometric identity:-

$\huge \boxed{Sin^2 A + Cos^2 A = 1}$

Now,

Now, Consider L. H. S

→$Sin^4 A - Cos^4 A$

→$(Sin^2A)^2 - (Cos^2A)^2$

$\huge \boxed{a^2 - b^2 = (a+b) (a-b) }$

→$(Sin^2 A + Cos^2A ) (Sin^2 A - Cos^2 A)$

→$1 ( Sin^2 A - Cos^2 A)$

→$Sin^2 A - Cos^2A$

→$Sin^2 A - ( 1-Sin^2 A)$

→$Sin^2 A - 1 + Sin^2 A$

→$2Sin^2 A -1$ proved...