Question

tan^2 x + 4 = 2sec^2 x + tanx

Answer 1

You have to prove the identity? @Yellowpanda

Answer 2

solve

Answer 3

Solve for x?

Answer 4

yes xD

Answer 5

Well the obvious approach here would be to benefit here from the following identity:\[\sec^2(x)=\tan^2(x)+1\]

Answer 6

Can you see yourself using that identity to solve for x? @Yellowpanda

Answer 7

not really (

Answer 8

Use that identity to replace sec^2(x), then bring the equation on one side. That way you'll have a quadratic so solve for and that will lead you to the answers for x.

Answer 9

ohh

Answer 10

okay lemme try that

Answer 11

\[\sec^2(x)=\tan^2(x) +1 \rightarrow \tan^2(x)+4=2(\tan^2(x)+1)+\tan(x)\]\[\rightarrow \tan^2(x)+4=2\tan^2(x)+2+\tan(x) \rightarrow \tan^2(x) + \tan(x) -2=0\]Now that we have a quadratic, can you solve for x? @Yellowpanda

Answer 12

\[Tan ^{2}x+4=2\sec ^{2}x + Tanx\]
Applying the formula Genius gave,
\[Tan ^{2}x + 4 =2(\tan ^{2}x+1) + Tanx\]\[Tan ^{2}x + 4 = 2Tan ^{2}x + 2 + Tanx\]
\[0=2Tan ^{2}x-Tan ^{2}x +2 - 4 + Tanx\]
\[0 = Tan ^{2}x -2 + Tanx\]
\[0 = Tan ^{2}x + Tanx - 2\]

Answer 13

yes XD i got it

Answer 14

thank you guys!!

Answer 15

Good job! :D @Yellowpanda

Answer 16

@Yellowpanda Give @genius12 a medal.