Question

10sin^2 alpha+6cos^2 alpha=7
find the value of cot alpha​

Answer 1

Answer:

$\huge\mathbb\fcolorbox{purple}{lavenderblush}{✰Answer}$

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Given that,

$\bf{10\:sin^2\alpha+6\:cos^2\alpha=7}10sin$

$\begin{gathered}\:\:\:\displaystyle{\sf{:\implies\:10\:sin^2\alpha+6(1-sin^2\alpha)=7}}\end{gathered}$

$\begin{gathered}\:\:\:{\sf{:\implies\:10\:sin^2\alpha+6-6\:sin^2\alpha=7}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:{\sf{:\implies\:4\:sin^2\alpha=7-6}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:{\sf{:\implies\sin^2\alpha=\frac{1}{4}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=√\frac{1}{4}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=±\frac{1}{2}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=\frac{1}{2}[\frac{π}{2} < \alpha < π]}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=sin(\frac{5π}{6})}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\alpha=\frac{5π}{6}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:{\sf{:\implies\cot\alpha=cot(\frac{5π}{6})}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:{\sf{:\implies\cot\alpha=\frac{1}{tan\frac{5π}{6}}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:{\sf{:\implies\cot\alpha=-√3}}\end{gathered}$

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Answer 2

The change in velocity in unit time is called acceleration.

Acceleration is a vector.

The direction of acceleration will be in the direction of change in velocity.

Its SI unit is metre / second ² abbreviated as m/s²

Answer 3

The change in velocity in unit time is called acceleration.

Acceleration is a vector.

The direction of acceleration will be in the direction of change in velocity.

Its SI unit is metre / second ² abbreviated as m/s²

Answer 4

The change in velocity in unit time is called acceleration.

Acceleration is a vector.

The direction of acceleration will be in the direction of change in velocity.

Its SI unit is metre / second ² abbreviated as m/s²

Answer 5

The change in velocity in unit time is called acceleration.

Acceleration is a vector.

The direction of acceleration will be in the direction of change in velocity.

Its SI unit is metre / second ² abbreviated as m/s²

Answer 6

The change in velocity in unit time is called acceleration.

Acceleration is a vector.

The direction of acceleration will be in the direction of change in velocity.

Its SI unit is metre / second ² abbreviated as m/s²