Question

The value of sin² 30° – cos² 30° is
2 points
(a) –1/2
(b) √3/2
(c) 3/2
(d) –2/3​

Answer 1

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

We know that :-

• sin 30° = 1/2
• cos 30° = √3/2

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

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

LCM = 4

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

$\implies \sf {\dfrac{ - 2}{4} }$

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

$\implies \sf {sin}^{2} 30 \degree - {cos}^{2} 30 \degree = \dfrac{ - 1}{2}$

Answer :

• option (a) -1/2 is correct

____________________

Trigonometric table :-

$\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3} }{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }& 1 & \sqrt{3} & \rm Not \: De fined \\ \\ \rm cosec A & \rm Not \: De fined & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm Not \: De fined \\ \\ \rm cot A & \rm Not \: De fined & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}$