Question

If 7 sin2 + 3 cos2 0 = 4, find the value of v3tan​

Answer 1

Correct Question

• If 7sin² + 3cos² θ = 4 then the value of tanθ is ?

━━━━━━━━━━━━━━━━━━━━━━━━━

ANSWER :

To find

• tanθ

━━━━━━━━━━━━━━━━━━━━━━━━━

Solution:

$\begin{gathered}\begin{gathered}\dashrightarrow \displaystyle \sf \: Dividing \: by \: cos²θ \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\dashrightarrow \displaystyle \sf \: 7 \tan^{2} θ \: + \: 3 \: = \: 4 \sec^{2} \: = 4(1 \: + \tan^{2} θ)\\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:3 \tan^{2} θ \: = 1 }} }\\ \\\end{gathered}\end{gathered}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ OR

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:\tan θ \: = ± \frac{1}{ \sqrt{3} } }} }\\ \\\end{gathered}\end{gathered}$

━━━━━━━━━━━━━━━━━━━━━━━━━