Question

if sin theta + sin square theta is equal to 1 show that cos square theta + Cos raise to 4 theta is equal to 1​

Answer 1

Step-by-step explanation:

Sin theta+sin sq.theta=1

Sin theta=1- sin sq.theta

Sin theta=cos sq. theta

1 equation

Cos sq. theta+cos^4 theta=1

LHS,

Cos sq.theta+cos power 4

Sin theta+sin sq.theta(from 1 equation)

1 ans.

Answer 2

sinA + sin²A = 1 ... (i) (given)

sinA = 1 - sin²A

sinA = cos²A ... (ii) (sin²A + cos²A = 1)

now,

cos²A + cos⁴A

= cos²A + (cos²A)²

= sinA + sin²A ... (from (ii))

= 1 ... (from (i))

Hence, cos²A + cos⁴A = 1.

... Hence, Proved!