Question

tan 2(teta) - cot 2(teta)=0

Answer 1

Is that

\[\tan ^{2}\theta - \cot ^{2}\theta = 0 \]

?

Answer 2

tan 2θ - cot 2θ =0

Answer 3

\[\tan(\theta) = \frac{ \sin(\theta ) }{ \cos(\theta) }\]\[\cot(\theta) = \frac{ \cos(\theta) }{ \sin(\theta) }\]

Answer 4

then cross multiplication?

Answer 5

Ok, try

\[\tan(2\theta) = \cot(2\theta) --> \frac{ \sin(2\theta) }{ \cos(2\theta) } = \frac{ \cos(2\theta) }{ \sin(2\theta) } \]

Cross multiply to obtain

\[\sin ^{2} (2\theta) = \cos ^{2}(2\theta)\]

I used various techniques from here. The method is up to you.

Answer 6

then bring cos to produce tan??

Answer 7

i got it...:)

Answer 8

give me the final answer please

Answer 9

\[\sin ^{2}(2\theta) = \cos ^{2}(2\theta) -> 2\sin ^{2}(2\theta) = \sin ^{2}(2\theta) + \cos ^{2}(2\theta)\]

\[2\sin ^{2}(2\theta) = 1\]

Using the results of trig identities the left becomes

\[1 - \cos(\theta) = 1 ==> \cos(4\theta) = 0 ==> 4\theta = \frac{ \pi }{ 2 } + k \pi\]

Answer 10

The last thing on the bottom left should read 1 - cos (4 theta) instead of 1 - cos (theta)