Question

the value of 2sin^2 30 -3 cos^2 45 + tan^2 60 + 3sin^2 90​

Answer 1

$\implies2 { \sin }^{2} 30\degree - 3 { \cos }^{2} 45\degree + { \tan }^{2} 60\degree + 3 { \sin }^{2} 90\degree$

Now put :-

• sin30° = 1/2

• Cos 45° = 1/√2

• tan 60° = √3

• sin90° = 1

$\implies2 { (\dfrac{1}{2}) }^{2} - 3 { ( \dfrac{1}{ \sqrt{2} } ) }^{2} + { (\sqrt{3} ) }^{2} + 3 {( 1) }^{2}$

$\implies(2 \times \dfrac{1}{4}) - 3 ( \dfrac{1}{2 } )+ {3} + 3$

$\implies( \dfrac{1}{2}) - ( \dfrac{3}{2 } )+ 6$

$\implies ( \dfrac{1 - 3}{2 } )+ 6$

$\implies ( \dfrac{ - 2}{2 } )+ 6$

$\implies - 1 + 6$

$\implies 5$

Answer : 5

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Trigonometric Table :-

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

Answer 2

Answer:

Ans is 5

Step-by-step explanation:

can refer the attachment