If u=sin-1(𝒙𝟐ା𝒚𝟐𝒙ା𝒚), then prove that x2𝝏𝟐𝒖𝝏𝒙𝟐 +𝟐𝒙𝒚 𝝏𝟐𝒖𝝏𝒙𝝏𝒚 𝒚𝟐 𝝏𝟐𝒈𝝏𝒚𝟐= tan3u

Prove the trigonometric identity 𝑐𝑜𝑠2𝐴 + 𝑠𝑖𝑛2𝐴 = 1

Verify the identity.cos(u) sec(u)tan(u) = cot(u)Use a Reciprocal Identity to rewrite the expression, and then simplify.cos(u) sec(u)tan(u) =  cos(u) sec(u)   =  cos(u) · 1cos(u) ·   =

Given 𝛼 = tan−1 𝑥, find the exact values of sin 𝛼 and cos 𝛼

If 𝑢 = 𝑥2 tan−1 𝑦𝑥 − 𝑦2 tan−1 𝑥𝑦 show that 𝜕2𝑢𝜕𝑥𝜕𝑦 = 𝑥2−𝑦2𝑥2+𝑦2 and 𝜕2𝑢𝜕𝑥𝜕𝑦 = 𝜕2𝑢𝜕𝑦𝜕𝑥.

Rewrite tansin−1u6 as an algebraic expression in u.=tansin−1u6