Question

Evaluate the following : 2cos² 60^ + 3sec² 30^ - 2tan² 45^ ÷ sin² 30^ + cos² 45^

Answer 1

Answer:

2cos² 60° + 3sec² 30° - 2tan² 45° ÷ sin² 30° + cos² 45° = 4

Step-by-step explanation:

cos 60° = 1/2

2cos² 60° = 2(1/4) = 1/2

$sec30° = \frac{2}{ \sqrt{3} }$

3sec² 30° =

$3( {\frac{2}{ \sqrt{3} })}^{2} = <strong>4</strong>$

tan45° = 1

2tan² 45° = 2(1) = 1

sin30° = 1/2

sin² 30° = 1/4

cos45° = 1/√2

cos² 45° = 1/2

2cos² 60° + 3sec² 30° - 2tan² 45° ÷ sin² 30° + cos² 45° $= \frac{1}{2} + 4 - 2 \div \frac{1}{2} + \frac{1}{2}$

$= \frac{1}{2} + 4 - 1 + \frac{1}{2}$

$= 4$