Question

sin x + sin square x is equal to 1 then find the value of cos square X + Cos^4 X​

Answer 1

AnswEr :

The value of the above expression is 1

Given,

sin x + sin²x = 1

We have to find the value of cos²x + cos⁴x

Now,

sin x + sin²x = 1

→ sin x = 1 - sin²x

→ sin x = cos²x

Thus,

cos²x + cos⁴x

→ cos²x + (cos²x)²

→ cos²x + (sin x)²

→ sin²x + cos²x (sin²∅ + cos²∅ = 1)

→ 1

Answer 2

Answer:

Given that

sinx + sin²x = 1

sinx = 1 - sin²x

We know that

1 - sin²x = cos²x

Now,

sinx = cos²x

To find:

cos²x + cos⁴x

Method 1 :

Substituting cos²x = sinx

sinx + (cos²x)²

= sinx + sin²x

It is already given that sinx + sin²x = 1

Now,

sinx + sin²x = 1

Method 2 :

cos²x + (cos²x)²

Substituting cos²x = sinx only for second term

cos²x + sin²x

Using first identity sin²x + cos²x = 1

cos²x + sin²x = 1

cos²x + cos⁴x = 1