Question

Prove that: 1 - sin to the power 4 A whole upon cos to the power 4 A = 1 + 2 tan to the power 2 A​

Answer 1

To prove the equation, we can rewrite sin^4A as (sin^2A)^2 and cos^4A as (cos^2A)^2. Then, substitute these values into the equation and simplify. Finally, use the identity 1 + tan^2A = sec^2A to further simplify the expression.

Step-by-step explanation:

To prove that 1 - sin4A / cos4A = 1 + 2tan2A,

we can start by expressing the left side of the equation in terms of sine and cosine.

Using the identity sin2A + cos2A = 1, we can rewrite sin4A as (sin2A)2 and cos4A as (cos2A)2.

Then, we can substitute these values into the equation and rearrange terms to simplify the expression.

Finally, by using the identity 1 + tan2A = sec2A, we can further simplify the expression to obtain the right side of the equation.