Question

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

Answer 1

$\bf{cos ^{2}45 ^ {\circ} - sin0 ^{ \circ} - sin30^{ \circ} + 2sin45 ^{ \circ} - sin90^{ \circ} }$

• cos 45° = 1/√2
• sin 0° = 0
• sin 30° = 1/2
• sin 45° = 1/√(2
• sin 90° = 1

$\longrightarrow \: \sf{ \bigg(\dfrac{1}{ \sqrt{2} } \bigg)^{2} - 0 - \dfrac{1}{2} + \bigg( 2 \times \dfrac{1}{ \sqrt{2} } \bigg) - 1 } \\ \\ \longrightarrow \: \sf{ \dfrac{1}{2 } - \dfrac{1}{2} + \dfrac{2}{ \sqrt{2} } - 1 } \\ \\ \longrightarrow \: \sf{ \cancel{ \frac{1}{2} } - \cancel{ \frac{1}{2} } + \frac{ \cancel{ \: 2}}{ \cancel{ \sqrt{2} }} - 1} \\ \\ \longrightarrow \: \sf{ \sqrt{2} - 1 } \\ \\ \longrightarrow \: \sf{1.41 - 1} \\ \\ \longrightarrow \: \boxed{ \bf{0.41}}$

Cos²45° - Sin0° - sin30° + 2sin45° - sin90° = 0.41

Answer 2

Given:-

The equation is

Cos²45 - Sin0 - sin30 + 2sin45 - sin90

To solve:-

Evaluate the given equation

Concept used:-

● Cos 45° = 1 / √2

● Sin 0° = 0

● Sin 30° = 1 / 2

● Sin 45° = 1 / √2

● Sin 90° = 1

Solution :-

$⇒( \frac{1}{ \sqrt{2} })^{2} - 0 - \frac{1}{2} (2 \times \frac{1}{ \sqrt{2} } - 1) \\ ⇒ \frac{1}{2} - \frac{1}{2} + \frac{2}{ \sqrt{2} } - 1 \\ ⇒ \frac{1}{2} - \frac{1}{2} + \frac{2}{ \sqrt{2} } - 1$

Cutting the equation , we get,

$\sqrt{2} - 1 \\ = 1.41 - 1 \\ = 0.41$

Final result :-

Cos²45 - Sin0 - sin30 + 2sin45 - sin90 = 0.41