trigonometry1

Start Your Free Trial

Tangent of double angle calculate the tangent of double angle sinx+cosx=1, tan2x=? cos2x=?

Expert Answers info

hala718 eNotes educator | Certified Educator

calendarEducator since 2008

write3,662 answers

starTop subjects are Math, Science, and Social Sciences

Given that: sinx + cosx = 1

We need to find tan 2x

We know that:

tan2x = 2tanx / (1-tan^2 x)

Then, we will determine tanx

Let us divide the equation by cosx

==> sinx + cosx = 1

==> (sinx/cosx) + cosx/cosx = 1/cosx

==> tanx +...

(The entire section contains 93 words.)

Unlock This Answer Now


check Approved by eNotes Editorial


giorgiana1976 | Student

sinx+cosx=1

If we'll divide by cos x:

sin x/cos x + 1= 1/cos x

tan x + 1= 1/cos x

tan x= 1/(cos x -1)

We could write the tangent of the double angle as:

tan 2x = tan (x+x)

tan 2x = (tan x + tan x)/[1-(tan x)^2]

tan 2x =  2tan x/[1-(tan x)^2]

tan 2x =2/(cos x -1)/[1-(1/cosa)+1][1+ (1/cosa)-1]

If we'll raise to square, we'll get:

(tan 2x)^2 + 1= 1/(cos 2x)^2 

cos 2x = 1/sqrt[(tan 2x)^2 + 1]

check Approved by eNotes Editorial