Question

How can I verify this identity?

Sin 2t - tan t = tan t cos 2t

Answer 1

you can start from the left side

Answer 2

sin(2t) - tan(t)
= 2 sin(t) cos(t) - tan(t)
= 2 sin (t) cos(t) - sin(t) / cos(t)

Answer 3

And then?

Answer 4

then make a common denominator

Answer 5

sin(2t) - tan(t)
= 2 sin(t) cos(t) - tan(t)
= 2 sin (t) cos(t) - sin(t) / cos(t)
= 2 sin (t) cos(t)*[cos(t)/ cos(t)] - sin(t) / cos(t)
= [2 sin (t) cos^2(t) - sin(t)] / cos(t)
= sin(t) ( 2cos^2(t) -1 ) / cos(t)

Answer 6

now you are very close to the conclusion

Answer 7

<rolling drums>
<growing suspense>
<sweaty palms>

so.... what do you have thus far?

Answer 8

hint: use substitition cos(2t) = 2cos^2(t) - 1

Answer 9

I am still stuck in (2 sin t cost t) - (sin / cos)