Mathematics: Verify the identity: (1 + tan^2x)(1 - sin^2x) = 1 i know the solution, but not the steps to get me the answers i need. i will need to know how to do this on my own for a test soon, so any explanations will be appreciated. solution, kinda: (1 + tan^2x)(1 - sin^2x) = sex^2x * cos^2x = 1/cos^2x = 1 here are some identities that i m pretty sure need to be used, but i m not sure how or in what context to use them. quotient identities: tan x = (sin x)/(cos x) cot x = (cos x)/(sin x) reciprocal identities:

Verify the identity: (1 + tan^2x)(1 - sin^2x)

Ответ:

xarianna2007

08.01.2022

$(1+\tan^2x)(1-\sin^2x)=\sec^2x(1-\sin^2x)$

which follows from the Pythagorean identity. The same identity tells you that

$\sec^2x(1-\sin^2x)=\sec^2x\cos^2x$

Finally, since $\sec x=\dfrac1{\cos x}$ (by definition), you're left with

$\sec^2x\cos^2x=\dfrac1{\cos^2x}\times\cos^2x=1$

0,0(0 оценок)

Ответ:

crystalxolotp4q3la

05.04.2023

Mathematics

Your answer is yes my g

0,0(0 оценок)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question