Question

What is the value of sin square 60 - cos square 60

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ { \sin}^{2} {60}^{ \circ} - { \cos}^{2} {60}^{ \circ} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ { \sin}^{2} {60}^{ \circ} - { \cos}^{2} {60}^{ \circ} }$

We know that

$\displaystyle \sf{ { \sin} {60}^{ \circ} = \frac{ \sqrt{3} }{2} }$

$\displaystyle \sf{ { \cos}^{} {60}^{ \circ} = \frac{1}{2} }$

Hence

$\displaystyle \sf{ { \sin}^{2} {60}^{ \circ} - { \cos}^{2} {60}^{ \circ} }$

$\displaystyle \sf{ = { \bigg( \frac{ \sqrt{3} }{2} \bigg)}^{2} - { \bigg( \frac{1 }{2} \bigg)}^{2} }$

$\displaystyle \sf{ = \frac{3}{4} - \frac{1}{4} }$

$\displaystyle \sf{ = \frac{3 - 1}{4} }$

$\displaystyle \sf{ = \frac{2}{4} }$

$\displaystyle \sf{ = \frac{1}{2} }$

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