Question

verify (tanx+1)^2 =(1+sin2x)sec^2x

Answer 1

(tanx+1)^2 = tan^2x + 2tanx + 1

= sin^2x + 2sinx + 1
----- -----
cos^2x cos x

= sin^2x + 2sinxcosx + cos^2x
-------------------------
cos^2 x

now use the identities sin^2x + cos^2x = 1 and 1/cos^2x = sec^2x

can you continue?

Answer 2

oh! also 2sinxcosx = sin2x

Answer 3

Thank you so much for replying! I am still kind of confused about how you got to your third step. Would you mind explaining it to me?

Answer 4

oh ok - we are converting to one fraction
the LCM of cos^2x and cos x = cos^2x
so we multiply each fraction by this LCM


eg sin^2x cos^2x = sin^2x
------ *
cos^2^x

Answer 5

Thank you! So from the step you left off at sin^2x+2sinxcosx+cos^2x / cos^2x. s=I used the pythagorean identities sin^2x+cos^2x to equal 1. so know I have 1+2sinxcosx / cos^2x. If this correct? If so I'm not sure where to go from here