Question

cos theta equal to root 10 find tan theta​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{tan\:\theta=\frac{3\iota}{\sqrt{10}}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies cos \: \theta = \sqrt{10} \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies tan \: \theta = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies tan \: \theta \\ \\ \tt: \implies \frac{sin \: \theta}{cos \: \theta} \\ \\ \tt: \implies \frac{sin \: \theta}{ \sqrt{10} } \\ \\ \tt \circ \: sin \: \theta = \sqrt{1-cos^{2} \: \theta } \\ \\ \tt \circ \: sin \: \theta = \sqrt{1- (\sqrt{10} )^{2} } \\ \\ \tt \circ \: sin \: \theta = \sqrt{1-10} \\ \\ \tt \circ sin \: \theta = \sqrt{-9}=\sqrt{9}\iota \\ \\ \tt: \implies \sqrt{\frac{9 }{ 10 }}\iota \\ \\ \green{\tt: \implies \frac{3\iota}{\sqrt{10} }} \\ \\ \green{\tt \therefore tan \: \theta = \frac{3\iota}{\sqrt{10} } }$

Answer 2

Given:-

cosθ = √10

To find:-

The value of tanθ.

Solution:-

We know that, cosθ = b/h

⇒b/h = √10

So, here b = √10 and h = 1

Here we see that b>h, which is impossible.

Moving ahead with an imaginary value, let the values remain as they are.

Now, tanθ = sinθ/cosθ

⇒tanθ = sinθ/√10

sinθ = √(1-cos²θ)

⇒sinθ = √[1-(√10)²]

⇒sinθ = √(-9)

Root of a negative number is impossible to be operated.

So, let √(-9) = √9 i

tanθ = √9 i/√10

$\boxed{\implies tan\theta = \frac{3 i}{\sqrt{10} } }$