Question

If sin A – cos A = 0, then the value of sin4 A + cos4 A.​

Answer 1

Step-by-step explanation:

Given :-

Sin A - Cos A = 0

To find :-

Find the value of Sin⁴ A + Cos⁴ A ?

Solution:-

Given equation is Sin A - Cos A = 0

=> Sin A = 0+ Cos A

=> Sin A = Cos A

=> Sin A = 1× Cos A

=> Sin A / Cos A = 1

=> Tan A = 1

=> Tan A = Tan 45°

=> A = 45°

Therefore, A = 45°

Now ,

Sin⁴ A + Cos⁴ A

=> (Sin 45°) ⁴ + (Cos 45°)⁴

=> (1/√2)⁴ + (1/√2)⁴

=> (1/4) + (1/4)

=> (1+1)/4

=> 2/4

=> 1/2

Answer:-

The value of Sin⁴ A + Cos⁴ A for the given problem is 1/2

Used formulae:-

• Sin A / Cos A = Tan A
• Tan 45° = 1
• Sin 45° = 1/√2
• Cos 45° = 1/√2