Question

(1+tanx)(1-tanx)+sec^2x

Answer 1

the answer is two, i am completely lost.

Answer 2

1-tan^x +sec^2x
Now can you solve?

Answer 3

HINT use trigonometric identity

Answer 4

ankit, so we have tangent raised to the x power?

Answer 5

sorry made a typo it is tan^2x

Answer 6

1-tan^2 x +sec^2 x = 2

Answer 7

\[1-\tan ^2x\]

Answer 8

?

Answer 9

yes

Answer 10

should i do sin^2x over cosine ^2x

Answer 11

NO there is one for tanx

Answer 12

1+tan^2x = sec^2x

Answer 13

so we bring the sec to the otherside? Would we attach a negative to it?

Answer 14

Try replacing sec^2 with 1+tan^2

Answer 15

oh, lol i see what you are saying

Answer 16

:)

Answer 17

so im left with two? the tangents cancel out?

Answer 18

wow, i over looked this problem if i am correct. Thank you for the help ankit. :)

Answer 19

no problem!

Answer 20

\[\large (1+\tan(x))(1-\tan(x))+\sec^2(x)\]\[\large 1-\tan^2(x) +\color{green}{\sec^2(x)}\]\[\large \color{green}{1+\cancel{\tan^2(x)}}+1-\cancel{\tan^2{x}}\]

Answer 21

Omg the lag. Good job Ankit.

Answer 22

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

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

Use the identity : \( \tan^2 x + 1 = \sec^2 x \) to replace \( \sec^2 x \) with \( \tan^2 x + 1 \)

\( 1 - \tan^2 x + \tan^2 x + 1= 2 \)

\(2 = 2\)