Question

sec^4theta - cos^4theta = 1- 2cos^2theta
prove it

Answer 1

hope this helps you ☺☺

Answer 2

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 ya ☺