Question

Evaluate the following
Cos²45 - Sin0 - sin30 + 2sin45 - sin90​

Answer 1

$\cos(45) = \frac{1}{ \sqrt{2} } \: \sin(0) = 0 \: \sin(30) = \frac{1}{2} \: \sin(45) = \frac{1}{ \sqrt{2} } \: \sin(90) = 1 \\ now \: substitute \: these \:values \: \frac{1}{2} - 0 - \frac{1}{2} + 2 \times \frac{1}{ \sqrt{2} } - 1 \\ = \sqrt{2} - 1$

Answer 2

Answer:

√2 - 1

Step-by-step explanation:

Cos 45° = 1/√2

Sin 0° = 0, Sin 30° = 1/2, Sin 45°= 1/√2, Sin 90°= 1

Now,

(1/√2)^2- 0- (1/2) + 2× (1/√2) - 1

(1/2) - (1/2) + (2/√2) -1

= (2/√2) -1

= (2 - √2)/√2

= (2√2 - 2)/ (√2×√2)

= [2 (√2-1)/ 2]

= √2 - 1