COS 2 Establish each identity cos40 cos4e6sinZgcosag sin9

COS- 2 Establish each identity cos(40) = cos4e-6sinZgcosag + sin#9 9. sin(20)+2sinag 2tan cos(20) sin (30) = 4cosag-1 COS -- 2 11. in-2 Use the Half-angle Formulas to find the e

Solution

8). cos(4) = cos(2 x 2) = cos²(2) - sin²(2)

= (cos² - sin²)² - (2sincos)²

= cos⁴ + sin⁴ - 2sin²cos² - 4sin²cos²  

= cos⁴ - 6sin²cos² + sin⁴

9) (sin2 + 2sin²)/cos2 = (2sincos + 2sinsin)/(cos² - sin²)

= (2sin(cos + sin))/((cos - sin)(cos + sin))

= 2sin/(cos - sin)

divide by cos in numerator and denominator,   

= 2tan/(1 - tan)

10) sin3/sin = (3sin - 4sin³)/sin

= 3 - 4sin²

= 3 - 4(1 - cos²)

= 4cos² - 1

11) sin²(/2)/sin² = ((1 - cos)/2)/(1 - cos²)

= ((1 - cos)/2)/((1 - cos)(1 + cos))

= 1/(2 + 2cos)