If fx=sec⁡θtan2⁡θ1θsec⁡xtan⁡xx1tan⁡x−tan⁡θ0 then f1θ is

f1(x)=000θsec⁡xtan⁡xx1tan⁡x−tan⁡θθ+sec⁡θtan2⁡θ1θsec⁡xtan⁡xsec2⁡x11tan⁡x−tan⁡θ0+sec⁡θtan2⁡θ1θsec⁡xtan⁡xx0sec2⁡x0f1(θ)=0+sec⁡θtan2⁡θ1θsec⁡θtan⁡θsec2⁡θ1100+sec⁡θtan2⁡θ1θsec⁡θtan⁡θθθsec2⁡θ0=−1

If fx=sec⁡θtan2⁡θ1θsec⁡xtan⁡xx1tan⁡x−tan⁡θ0 then f1θ is

f1(x)=000θsec⁡xtan⁡xx1tan⁡x−tan⁡θθ+sec⁡θtan2⁡θ1θsec⁡xtan⁡xsec2⁡x11tan⁡x−tan⁡θ0+sec⁡θtan2⁡θ1θsec⁡xtan⁡xx0sec2⁡x0f1(θ)=0+sec⁡θtan2⁡θ1θsec⁡θtan⁡θsec2⁡θ1100+sec⁡θtan2⁡θ1θsec⁡θtan⁡θθθsec2⁡θ0=−1

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $f (x) = |\begin{array}{ccc} \sec θ & \tan^{2} θ & 1 \\ θ \sec x & \tan x & x \\ 1 & \tan x - \tan θ & 0 \end{array}| then f^{1} (θ)$ is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

– 1

independent of $θ$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$f^{1} (x) =$ $|\begin{array}{ccc} 0 & 0 & 0 \\ θ \sec x & \tan x & x \\ 1 & \tan x - \tan θ & θ \end{array}| + |\begin{array}{ccc} \sec θ & \tan^{2} θ & 1 \\ θ \sec x \tan x & \sec^{2} x & 1 \\ 1 & \tan x - \tan θ & 0 \end{array}| + |\begin{array}{ccc} \sec θ & \tan^{2} θ & 1 \\ θ \sec x & \tan x & x \\ 0 & \sec^{2} x & 0 \end{array}|$

$f^{1} (θ) =$ $0 + |\begin{array}{ccc} \sec θ & \tan^{2} θ & 1 \\ θ \sec θ \tan θ & \sec^{2} θ & 1 \\ 1 & 0 & 0 \end{array}| + |\begin{array}{ccc} \sec θ & \tan^{2} θ & 1 \\ θ \sec θ & \tan θ & θ \\ θ & \sec^{2} θ & 0 \end{array}| = - 1$