Question

last one prove the identity show all work 2tanx /1+tan^2x=sin2x

Answer 1

thats 1+\(tan^2x\) in denominator, right ?

Answer 2

else it can't be proved

Answer 3

yes sorry it was my mistake

Answer 4

so write tanx in terms of sin x and cos x, both in num and denom

Answer 5

so 2sinx/cosx/1+cos^2x/sin^2x

Answer 6

yeah, simplify it

Answer 7

idk how to do that

Answer 8

lets take denominator only
\(1+ \frac{sin^2x}{cos^2x }= ? \)

Answer 9

okay

Answer 10

\(\huge 1+ \frac{sin^2x}{cos^2x }= \frac{sin^2x+cos^2x}{cos^2x}=?\)

Answer 11

okay

Answer 12

what numerator equals there ^ ?

Answer 13

1

Answer 14

yes, so in denominator , its only 1/cos^2 x
now what is 2sin x/ cos x /(1/cos^2 x ) = ?

Answer 15

divide by 1/cos^2 x = multiply by cos^2 x
so 2sin x/ cos x /(1/cos^2 x ) = 2 sin x cos^2x / cos x = ?

Answer 16

2sinxcos^2 x?

Answer 17

one cos x will cancel from numerator, right ?

Answer 18

yea

Answer 19

and sin 2x = 2sin x cos x is a standard formula

Answer 20

ok thank you so much thats all for today thanks for ur help have a great night

Answer 21

welcome ^_^
sweet dreams :)

Answer 22

thanks same to you