Question

find the principal solution of the equation tan x + cot x = 2 sec x​

Answer 1

Step-by-step explanation:

ANSWER

cotx=−

3

We know, cot

6

π

=

3

Therefore, cot(π−

6

π

)=−cot

6

π

=−

3

and cot(2π−

6

π

)=−cot

6

π

=−

3

cot

6

5π

=−

3

and cot

6

11π

=−

3

Therefore, the principal solutions are x=

6

5π

and

6

11π

.

Now, cotx=cot

6

5π

tanx=tan

6

5π

x=nπ+

6

5π

Therefore, the general solution is x=nπ+

6

5π

,n∈Z.