Question

Value of sin square 30°-cos square 30°

Answer 1

$\sin^230^\circ-\cos^230^\circ=-\frac{1}{2}$

Step-by-step explanation:

Given : Expression $\sin^230^\circ-\cos^230^\circ$

To find : The value of the expression ?

Solution :

$\sin^230^\circ-\cos^230^\circ$

We know by trigonometric values,

$\sin30^\circ=\frac{1}{2}$ and $\cos 30^\circ=\frac{\sqrt3}{2}$

Substitute in the expression,

$\sin^230^\circ-\cos^230^\circ=(\frac{1}{2})^2-(\frac{\sqrt3}{2})^2$

$\sin^230^\circ-\cos^230^\circ=\frac{1}{4}-\frac{3}{4}$

$\sin^230^\circ-\cos^230^\circ=-\frac{2}{4}$

$\sin^230^\circ-\cos^230^\circ=-\frac{1}{2}$

#Learn more

The value of sin square 60 + cos square 30 is​

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Answer 2

Answer:

Substitute in the expression,

\sin^230^\circ-\cos^230^\circ=(\frac{1}{2})^2-(\frac{\sqrt3}{2})^2sin

2

30

∘

−cos

2

30

∘

=(

2

1

)

2

−(

2

3

)

2

\sin^230^\circ-\cos^230^\circ=\frac{1}{4}-\frac{3}{4}sin

2

30

∘

−cos

2

30

∘

=

4

1

−

4

3

\sin^230^\circ-\cos^230^\circ=-\frac{2}{4}sin

2

30

∘

−cos

2

30

∘

=−

4

2

\sin^230^\circ-\cos^230^\circ=-\frac{1}{2}sin

2

30

∘

−cos

2

30

∘

=−

2

1