Number of real solutions of the equation (tan x +1)(tan x + 3)(tan x + 5)(tan x + 7) = 33

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

will be two in the interval $[- π / 2, π / 2]$

will be four in the interval $[- π / 2, π / 2]$

will be three in the interval $[- π / 2, π]$

will be four in the interval $[- π / 2, π]$

answer is A, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} (\tan^{2} x + 8 \tan x + 15) (\tan^{2} x + 8 \tan x + 7) = 33 \\ Let \tan^{2} x + 8 \tan x = p (p + 15) (p + 7) = 33 \\ \Rightarrow p = - 18 (rejected) or p = - 4 \\ \Rightarrow \tan^{2} x + 8 \tan x + 4 = 0 \\ So \tan x + 4 = \pm \sqrt{12} \\ \Rightarrow \tan x = - 4 + \sqrt{12} or - 4 - \sqrt{12} \end{array}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE