"Find the general solution: 1−tan2(x)1+tan2(x)=1−2sin2(x)" solved and explained

Secondary
Geometry
Trigonometry
Trigonometric equations and identities

Aneeka Hunt

Answered question

2020-10-23

Find the general solution:

1 - \frac{\tan^{2} (x)}{1} + \tan^{2} (x) = 1 - 2 \sin^{2} (x)

Answer & Explanation

doplovif

Skilled2020-10-24Added 71 answers

\tan^{2} x = \frac{\sin^{2} x}{\cos^{2} x} and \cos^{2} = 1 - \sin^{2} x and \cos^{2} x + \sin^{2} x = 1

therefore

1 - \frac{\frac{\sin^{2} x}{\cos^{2} x}}{1} + (\frac{\sin^{2} x}{\cos^{2} x})

then make the fractions of the top and bottom common by timeing by cosx therefore

\frac{\cos^{2} x - - \sin^{2} x}{\cos^{2} x + \sin^{2} x}

therefore

\cos^{2} x - \frac{\sin^{2} x}{1} = \cos^{2} x - \sin^{2} x

\cos^{2} = 1 - \sin^{2}

therefore

(1 - \sin^{2} x) - \sin^{2} x = 1 - 2 \sin^{2} x

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?

Product

Company

Connect with us

Get Plainmath App

Google Play

Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus

Cyprus reg.number: ΗΕ 419361

E-mail us: support@plainmath.net

Our Service is useful for:

Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD.