Q32 of 40 Page 1

If sin θ + cos θ = √3, then prove that tan θ + cot θ =1

OR


Evaluate.



Given - sin θ + cos θ = √3


To Prove - tan θ + cot θ =1


Property - sin2 θ + cos2 θ = 1


Answer Given equation –


sin θ + cos θ = √3


squaring on both sides,


∴ (sin θ + cos θ)2 = 3


∴ sin2 θ + cos2 θ + 2sin θ. cos θ = 3


∴ 1 + 2sin θ. cos θ = 3 ………( sin2 θ + cos2 θ = 1)


∴ 2sin θ. cos θ = 2


∴ sin θ. cos θ = 1 ………(1)


Now,


L.H.S. = tan θ + cot θ




………from (1)


= 1


= R.H.S.


∴ L.H.S. = R.H.S.


Hence Proved !!!


OR


Properties –


1. cos θ = sin (90⁰ – θ)


2. tan θ = cot (90⁰ – θ)


3. sin2 θ + cos2 θ = 1


4. tan θ. cot θ = 1


Answer –




………by properties given above




………by properties given above


= 1 + 2


= 3


More from this chapter

All 40 →
30

Obtain all the zeros of the polynomial x4+4x3-2x2-20x-15, if two of its zeroes are √5 and -√5.

 31

Two friends Seema and Aditya work in the same office at Delhi. In the Christmas vacations, both decided to go to their hometowns represented by Town A and Town B respectively in the figure given below. Town A and Town B are connected by trains from the same station C (in the given figure)in Delhi. Based on the given situation, answer the following questions:


(i) Who will travel more distance, Seema or Aditya, to reach to their hometown?


(ii) Seema and Aditya planned to meet at a location D situated at a point D. represented by the mid-point of the line joining the points represented by Town A and Town B. Find the coordinates of the point represented by the point D.


(iii) Find the area of the triangle formed by joining the points represented by A, B and C.


 33

Sides of a right triangular field are 25m, 24m and 7m. At the three corners of the field, a cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the field. Find the area of the field that cannot be grazed by these animals.

 34

A TV reporter was given a task to prepare a report on the rainfall of the city Dispur of India in a particular year. After collecting the data, he analyzed the data and prepared a report on the rainfall of the city. Using this report, he drew the following graph for a particular time period of 66 days.


Based on the above graph, answer the following questions:


(i) Identify less than type ogive and more than type ogive from the given graph.


(ii) Find the median rainfall of Dispur


(iii) Obtain the Mode of the data if mean rainfall is 23.4cm