Question

If sin⁴ A - cos⁴ A = 1 and 0 < A <_ 90°, then A =​? ( The answer is 45°). Just tell the process​

Answer 1

Step-by-step explanation:

If sin⁴ A - cos⁴ A = 1

(sin^2 A- cos^2 A )(sin^2 A+cos^2 A)=1

we know that,

sin^2 A+cos^2 A)=1

putting in above equation we get:

sin^2 A-cos^2 A)=1

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

1-cos^2 A-cos^2 A=1

cos^2 A = 0

cos A =0------(1)

we know that ,

cos 90°=0------(2)

From (1) and (2),

A=90°

A cannot be 45 as sin 45 = cos 45 =1/√2

so sin^4 45°- cos ^4 45° =0

when A=45°

Answer 2

Answer:

Given that,

sinA - cosA = 0

⇒ sinA = cosA

⇒ sinA/cosA = 1

⇒ tanA = 1

⇒ tanA = tan45°

⇒ A = 45°

∴ sin⁴A + cos⁴A

= sin⁴45° + cos⁴45°

= (1/√2)⁴ + (1/√2)⁴

= 1/4 + 1/4

= 2/4

= 1/2