[tex]\bf\underline{Question}:-[/tex]
[tex] \\ [/tex]
2) The value of 3 cosec² θ - 3 cot² θ - 2 is ______
[tex] \\ [/tex]
(a) - 2
(b) 0
(c) 1
(d) 2
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[tex]\bf\underline{Question}:-[/tex]
[tex] \\ [/tex]
2) The value of 3 cosec² θ - 3 cot² θ - 2 is ______
[tex] \\ [/tex]
(a) - 2
(b) 0
(c) 1
(d) 2
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Answer:
The correct answer is option (c) .
Step-by-step explanation:
Since we know the identity [tex]\cos ec^2\theta-\cot^2\theta=1[/tex]
Therefore [tex]3\cos ec^2\theta-3\cot^2\theta-2[/tex]
[tex]=3(\cos ec^2\theta-\cot^2\theta)-2\\[/tex]
[tex]=3(1)-2\\[/tex], using above formula
[tex]=3-2\\=1[/tex]
Verified answer
[tex]\bf\underline{Question:-}[/tex]
⠀
: The value of 3 cosec² θ - 3 cot² θ - 2 is ___
(a) - 2
(b) 0
(c) 1
(d) 2
⠀
[tex] \bf \underline{Solution :-}[/tex]
⠀
We know the identity that :
[tex] \bigstar \underline{ \boxed{ \sf {cosec}^{2} \theta - {cot}^{2} \theta = 1}} \bigstar[/tex]
Using this identity, we have :-
[tex] \sf\implies3 {cosec}^{2} \theta - 3 {cot}^{2} \theta - 2 \\ \\ \sf \implies 3( {cosec}^{2} - {cot}^{2} ) - 2 \: \: \: \\ \\ \sf \implies 3(1) - 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies3 - 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \bigstar\underline{ \boxed{{1}}} \bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Therefore the correct option is (c) 1.
⠀
[tex] \boxed{ \begin{array}{cc} \sf \underline{ Some \: important \: Identities : - } \\ \\ \sf1. \: {sin}^{2} \theta + {cos}^{2} \theta = 1 \: \: \: \: \\ \\ \sf 2. \: 1 - {cos}^{2} \theta = {sin}^{2} \theta \: \: \: \\ \\ \sf3. \: 1 - {sin}^{2} \theta = {cos}^{2} \theta \: \: \: \: \\ \\ \sf4. \: 1 + {tan}^{2} \theta = {sec}^{2} \theta \: \: \: \\ \\ \sf5. \: {sec}^{2} \theta - {tan}^{2} \theta = 1 \: \: \: \: \\ \\ \sf6. \: 1 + {cot}^{2} \theta = {cosec}^{2} \theta \\ \\ \sf7. \: {cosec}^{2} \theta - {cot}^{2} \theta = 1 \end{array}}[/tex]
⠀
Trigonometry Table :-
[tex] \begin{gathered} \Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} $ \sin $ & 0 & $\dfrac{1}{2 }$ & $\dfrac{1}{ \sqrt{2} }$ & $\dfrac{ \sqrt{3}}{2}$ & 1 \\ \cline{1-6} $ \cos $ & 1 & $ \dfrac{ \sqrt{ 3 }}{2} } $ & $ \dfrac{1}{ \sqrt{2} } $ & $ \dfrac{ 1 }{ 2 } $ & 0 \\ \cline{1-6} $ \tan $ & 0 & $ \dfrac{1}{ \sqrt{3} } $ & 1 & $ \sqrt{3} $ & $ \infty $ \\ \cline{1-6} \cot & $ \infty $ &$ \sqrt{3} $ & 1 & $ \dfrac{1}{ \sqrt{3} } $ &0 \\ \cline{1 - 6} \sec & 1 & $ \dfrac{2}{ \sqrt{3}} $ & $ \sqrt{2} $ & 2 & $ \infty $ \\ \cline{1-6} \cosec & $ \infty $ & 2 & $ \sqrt{2 } $ & $ \dfrac{ 2 }{ \sqrt{ 3 } } $ & 1 \\ \cline{1 - 6}\end{tabular}} \end{gathered}[/tex]
Note :- To view the trigonometry table kindly view it from the website or as for the app you can refer to the attachment.