Question

if sin x + sin square x is equal to 1 then the value of cos square X + Cos ^ 4 x is option 80 option b two option C one option d 3 ​

Answer 1

Answer:

Option C is correct

Step-by-step explanation:

Given :

To find the value of :

cos² x + cos⁴ x , if

sin x + sin² x = 1

Solution :

We know that,

sin² x + cos² x = 1

⇒ cos² x = 1 - sin² x ...(1)

___

sin x + sin² x = 1

⇒ sin x = 1 - sin² x ... (2)

By (1) & (2),

We get,

⇒ sin x = cos² x ...(3)

___

sin x + sin² x = 1

By substituting sin x = cos² x,

We get,

⇒ (cos² x) + (cos² x)² = 1

⇒ cos² x + cos⁴ x = 1

∴ Option C is correct