Question

sin theta + cos theta is equal to root 3 then prove that tan theta + cot theta is equal to 1​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Given :

sin Ф + cos Ф = √ 3

Squaring on both side :

sin² Ф + cos² Ф + 2  sin Ф cos Ф = 3

2 sin Ф cos Ф = 3 - 1

sin Ф cos Ф = 1  .... ( i )

tan Ф + cot Ф = 1

L.H.S. = tan Ф + cot Ф

= > sin Ф / cos Ф + cos Ф  / sin Ф

= > sin² Ф + cos² Ф / sin Ф cos Ф

= > 1 /  sin Ф cos Ф

From ( i )

= > 1 / 1

= > 1

L.H.S. = R.H.S.

Therefore , proved.