Question

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Question : If cosØ + cos²Ø = 1 then prove that sin²Ø + sin⁴Ø = 1.


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Answer 1

Answer:

sin⁴ Ø + sin² Ø = 1  [ Proved ]

Explanation:

Given :

cos Ø + cos² Ø =  1

Rewrite as :

cos Ø  =  1 - cos² Ø  

Now using  1 - cos² Ø  = sin² Ø

cos Ø = sin² Ø

Squaring on both side :

cos² Ø = sin⁴ Ø

Again using cos² Ø = 1 - sin² Ø

1 - sin² Ø = sin⁴ Ø

sin⁴ Ø + sin² Ø = 1

Hence proved .

Answer 2

Answer:

/* Here I am using A instead of Phi. */

Given cosA + cos²A = 1

=> cosA + 1-sin²A = 1

=> cosA = 1-1+sin²A

=> cosA= sin²A ---(1)

Now,

LHS = sin²A+ sin⁴A

= sin²A + (sin²A)²

= sin²A + (cosA)² /* From(1)*/

= sin²A + cos²A

= 1

= RHS

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