Question

4 Sin26° COS 26° ________________= cos ² 26 ° - COS²64°

Answer 1

$\frac{4Sin26^{0}Cos26^{0}}{Cos^{2}26^{0}-Cos^{2}64^{0}} =\frac{2*(2Sin26^{0}Cos26^{0})}{Cos^{2}26^{0}-Cos^{2}(90^{0}-26^{0})}=\frac{2Sin52^{0}}{Cos^{2}26^{0}-Sin^{2}26^{0}}=\frac{2Sin52^{0}}{Cos52^{0}}=2tg52^{0}$

Answer 2

To simplify the expression on the left side, we can use the double-angle identity for cosine:

1. Double-angle identity for cosine: cos(2θ) = 2cos²(θ) - 1

Let's simplify the left side step by step:

1. 4 * sin(26°) * cos(26°)

Now, using the double-angle identity for cosine (θ = 26°):

2. cos(2 * 26°) = 2 * cos²(26°) - 1

Now we have:

4 * sin(26°) * cos(26°) = 2 * cos²(26°) - 1

Next, let's work on the right side of the equation:

1. cos²(26°) - cos²(64°)

Now, we can use the difference of squares identity:

2. a² - b² = (a + b)(a - b)

where a = cos(26°) and b = cos(64°).

Applying this identity:

cos²(26°) - cos²(64°) = (cos(26°) + cos(64°))(cos(26°) - cos(64°))

Now, the equation becomes:

4 * sin(26°) * cos(26°) = 2 * cos²(26°) - 1 = (cos(26°) + cos(64°))(cos(26°) - cos(64°))

The equation is now simplified, but to proceed further and find the values, we need more information or values for sin(26°), cos(26°), and cos(64°).