1 + sec 2 x sin 2 x =, sin 2 x, sin 2 x, tan 2 x, sec 2 x

Let f x = 1 + sec 2 x sin 2 x ⇒ f x = 1 + sin 2 x cos 2 x ∵ sec x = 1 cos x ⇒ f x = 1 + tan 2 x ∵ tan x = sin x cos x ⇒ f x = sec 2 x

1 + sec 2 x sin 2 x =

Search any question & find its solution

Question: Answered & Verified by Expert

1 + \sec^{2} x \sin^{2} x =

MathematicsTrigonometric Ratios & IdentitiesAP EAMCETAP EAMCET 2022 (04 Jul Shift 2)

Options:

A $\sin 2 x$
B $\sin^{2} x$
C $\tan^{2} x$
D $\sec^{2} x$

Solution:

2993 Upvotes Verified Answer

The correct answer is:

\sec^{2} x

Let
$f (x) = 1 + \sec^{2} x \sin^{2} x$
$\Rightarrow f (x) = 1 + (\frac{\sin^{2} x}{\cos^{2} x})$
$[∵ \sec x = \frac{1}{\cos x}]$
$\Rightarrow f (x) = 1 + \tan^{2} x$
$[∵ \tan x = \frac{\sin x}{\cos x}]$
$\Rightarrow f (x) = \sec^{2} x$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play