Question

find the numerical value
​

Answer 1

Answer:

$\frac{13}{4}$

Step-by-step explanation:

Given :

to find the value of :

Sin² 45° + Cos² 150° + tan² 120° + Cos 180°

Solution :

We know that,

sin 45° = $\frac{1}{\sqrt{2} }$

cos 150° = cos (90° + 60°) = - sin 60° = $\frac{-\sqrt{3}}{2}$

tan 120° = tan (90° + 30°) = - cot 30° = $-\sqrt{3}$

cos 180° = cos (90° + 90°) = -sin 90° = -1

∴ Sin² 45° + Cos² 150° + tan² 120° + Cos 180°

⇒ $(\frac{1}{\sqrt{2}})^2 + (-\frac{\sqrt{3}}{2})^2 + (-\sqrt{3})^2 + (-1)$

⇒ $\frac{1}{2} + \frac{3}{4} + 3 - 1$

⇒ $\frac{2}{4} + \frac{3}{4} + 2$

⇒ $\frac{5}{4} + \frac{8}{4} = \frac{13}{4}$