Question

Solve tan theta + sec theta = root3​

Answer 1

Answer:

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Answer 2

Answer:

Ф = 2 n π + π / 6  OR  2 n π - π / 2 ,  n € Z

Step-by-step explanation:

Given :

tan Ф + sec Ф = √ 3

sin Ф / cos Ф + 1 / cos Ф = √ 3

sin Ф + 1 = √ 3 cos Ф

√ 3 cos Ф - sin Ф = 1

r = √ ( ( √ 3 )² + 1² ) = 2

Dividing by 2 both side we get :

√ 3 / 2 cos Ф - 1 / 2 sin Ф = 1 / 2

cos Ф cos π / 6 - sin Ф sin π / 6 = 1 / 2

Using identity cos ( A + B ) = cos A cos B - sin A sin B

cos ( Ф + π /6 ) = cos π / 3

On comparing we get :

Ф + π / 6 = π / 3

Ф = π / 6

We know if :

cos Ф = cos α

= > Ф = 2 n π ± α where n € Z

So , general solution is as :

= > Ф = 2 n π + π / 6 n € Z  or

= > Ф = 2 n π - π / 2 ,  n € Z

Therefore we get answer.