Question

find the value of
${ \sin }^{2} 30 - { \cos }^{2} 30$
​

Answer 1

Step-by-step explanation:

sin^2 30-cos^2 30.

(1/2)^2 - (√3/2)^2.

1/4 -3/4

= -1/2.

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Answer 2

$\large \fbox{ \: \sf \red{ A}n \blue{s}w \pink{e}r : \sf \: \: \sf \underline{}}$

$\star\: \: \sf { \sin }^{2} (30) - { \cos }^{2} (30) = - \frac{1}{2}$

$\large \fbox{ \: \sf \red{ S}o \blue{l}u \pink{t}i \green{o}n: \: \: \sf \underline{}}$

$\sf \hookrightarrow { \sin }^{2} (30) - { \cos }^{2} (30) \\ \\ \sf \hookrightarrow { (\frac{1}{2}) }^{2} - {( \frac{ \sqrt{3} }{2}) }^{2} \\ \\ \sf \underline{ Taking \: LCM \: , \: we \: obtain \: \: } \\ \\ \sf \hookrightarrow \frac{1}{4} - \frac{3}{4} \\ \\ \sf \hookrightarrow \frac{1 - 3}{4} \\ \\ \sf \hookrightarrow - \frac{ \cancel{ 2}}{ \cancel{4}} \\ \\ \sf \hookrightarrow - \frac{ 1}{2}$

Hence , the final value is -1/2