Question

if Sin A + sin square is equals to cos square A then prove that cos 6 is minus 4 cos4+ 8 cos square A is equals to 4​

Answer 1

Answer:

Step-by-step explanation:

Given that,

sin²∅ + sin∅ = 1

To prove :- cos²∅ + cos⁴∅ = 1

Proof :-

Here we are given

sin²∅ + sin∅ = 1

But we know that sin²∅ + cos²∅ = 1

So we can equate them

=> sin²∅ + sin∅ = sin²∅ + cos²∅

=> sin∅ = sin²∅ + cos²∅ - sin²∅

=> sin∅ = cos²∅

Now we know that, cos²∅ = sin∅

squaring both sides,

(cos²∅)² = (sin∅)²

=> cos⁴∅ = sin²∅

We have to show that cos²∅ + cos⁴∅ = 1

We have derived that, cos²∅ = sin∅ and cos⁴∅ = sin²∅

So substituting the value,

cos²∅ + cos⁴∅ = 1

=> sin∅ + sin²∅ = 1

=> 1 = 1 (since it's given that sin∅ + sin²∅ = 1)

L.H.S = R.H.S

Hence Proved :)