Question

2cot^2(60°)+3ain^2(30°)+2cos^2(90°) evaluate
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Answer 1

Answer:5/3Step-by-step explanation:2cot^2(60°) + 3tan^2(30°) + 2cos^2(90°) => 2(1/3) + 3(1/3) + 2(0)

=> 2/3 + 1 + 0=> 5/3

Hope you understand it.

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Thanks me

Answer 2

We have to find the value of the following expression :-

$\implies2 \: {cot}^{2} (60\degree) + 3{sin}^{2}(30\degree) + 2{cos}^{2}(90\degree)$

We know that :-

• Cot 60° = 1/√3

• Sin 30° = 1/2

• Cos 90 = 0

Now put the above values in the given expression :-

$\implies2 \: { (\dfrac{1}{ \sqrt{3} } )}^{2} + 3{( \dfrac{1}{2} )}^{2} +( 2 \times 0)$

$\implies2 \: { (\dfrac{1}{ 3 } )} + 3{( \dfrac{1}{4} )}+0$

$\implies \: { \dfrac{2}{ 3 } } + {\dfrac{3}{4} }$

LCM of 3 and 4 = 12

$\implies \: { \dfrac{8 + 9}{ 12 } }$

$\implies \: { \dfrac{17}{ 12 } }$

Answer :

${ \dfrac{17}{ 12 } }$

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

1. Cosθ = base / hypotenuse

2. cossecθ = 1/ sinθ

3. sec θ = 1/cosθ

4. Cotθ = 1/ tanθ

5. Sin²θ+ Cos²θ= 1

6. Sec²θ - tan²θ = 1

7. cosec ²θ - cot²θ = 1

8. sin(90°−θ) = cos θ

9. cos(90°−θ) = sin θ

10. tan(90°−θ) = cot θ

11. cot(90°−θ) = tan θ

12. sec(90°−θ) = cosec θ

13. cosec(90°−θ) = sec θ

14. Sin2θ = 2 sinθ cosθ

15. cos2θ = Cos²θ- Sin²θ

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