Question

Value of sin^2 30° - cos^30°

Answer 1

Answer:

-1/2

Step-by-step explanation:

sin²30° - cos²30°

= (1/2)² - (√3/2)²

= 1/4 - 3/4

= -2/4

= -1/2

Answer 2

Correct Question :

Find the value of

Sin² 30° -cos² 30°

$\red{\huge{\boxed{\sf{Solution:}}}}$

Let's look at some values

$\begin{array}{| c | c | c | c | c | c |}\cline{1-6} \bf Angles & \bf 0^{o} & \bf 30^{o} & \bf 45^{o} & \bf 60^{o} & \bf 90^{o} \\\cline{1-6} \tt Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}}& \dfrac{\sqrt{3}}{2}& 1\\\cline{1-6} \tt cos \theta & 1 & \dfrac{\sqrt{3}}{2} &\dfrac{1}{\sqrt{2}}&\dfrac{1}{2}&0\\\cline{1-6} \tt tan \theta & 0 & \dfrac{1}{\sqrt{3}} & 1& \sqrt{3} & \infty \\\cline{1-6} \tt cosec \theta & \infty & 2 & \sqrt{2} & \dfrac{2}{\sqrt{3}} &1\\\cline{1-6} \tt sec \theta & 1 & \dfrac{2}{\sqrt{3}} & \sqrt{2} & 2 & \infty \\\cline{1-6} \tt cot \theta & \infty & \sqrt{3} &1& \dfrac{1}{\sqrt{3}} &0\\\cline{1-6}\end{array}$

Here, '$\red{\infty}$' stands for

undefined(not defined) values.

$\rule{200}2$

$\sf\sin{}^{2}30\degree-\cos{}^{2}30\degree$

$\sf=(\dfrac{1}{2})^2-(\dfrac{\sqrt{3}}{2})^2$

$\sf=\dfrac{1}{4}-\dfrac{3}{4}$

$\sf=\dfrac{\cancel{-2}}{\cancel{4}}$

$\sf=\dfrac{-1}{2}$