Question

(1+cos^2A)(1-cosA)(1-cosA)

Answer 1

☞ (1 + cos²A) (1 - cosA) (1 + cosA)

Identities used :

1. (a + b) (a - b) = a² - b²
2. 1 - cos²A = sin²A

Method :

(1 + cos²A) (1 - cosA) (1 + cosA)

⇒(1 + cos²A) (1² - (cosA)²)

⇒(1 + cos²A) (1 - cos²A)

⇒ (1 + cos²A) (sin²A)

⇒ sin²A + sin²A.cos²A

Taking sin²A as a common factor,

sin²A(1 + cos²A)

Additional information:

• Sine of an angle is defined as Opposite side of an angle θ divided by Hypotenuse
• Cosecant of an angle is defined as the adjacent side of an angle θ divided by Hypotenuse
• Tangent of an angle is defined as sinθ by cosθ