Question

9. prove that

prove that sin^4theta +cos^4 theta=1-2cos^2 theta +2cos^4theta​

Answer 1

Hi there

We have

Sin⁴∅ - cos⁴∅

To prove ⇒ 1 - 2cos²∅

Proof :-

From :- LHS

sin⁴∅ - cos⁴∅

⇒ ( sin²∅) ² - ( cos²∅ ) ²

⇒ ( sin²∅ + cos²∅ ) ( sin²∅ - cos²∅ )

[ since , ( a + b ) ( a- b ) = a² - b² ]

and [ sin²∅ + cos²∅ = 1 ]

⇒ so, ( 1 ) ( 1 - cos²∅ - cos ²∅ )

[ since 1- cos²∅ = sin²∅ ]

⇒ 1 - 2 cos²∅ [ This is what we had to proof ]

Hope this helps :-)