**Chapter 2 Trigonometry – I Ex 2.2**

## Chapter 2 Trigonometry – I Ex 2.2

**Question 1.**

A lies in the 2nd quadrant.

We know that,

B lies in the 4th quadrant,

**Question 2.If and A, B are angles in the second quadran, then prove that 4cosA + 3 cos B = -5Solution:**

Since B lies in the second quadrant, cos B < 0

**Question 3.Solution:**

**Question 4.Eliminate 0 from the following:i. x = 3sec θ, y = 4tan θii. x = 6cosec θ,y = 8cot θiii. x = 4cos θ – 5sin θ, y = 4sin θ + 5cos θiv. x = 5 + 6 cosec θ,y = 3 + 8 cot θv. x = 3 – 4tan θ,3y = 5 + 3sec θSolution:**

i. x = 3sec θ, y = 4tan θ

∴ 16x

^{2}– 9y

^{2}= 144

ii. x = 6cosec θ and y = 8cot θ

.’. cosec θ = and cot θ =

We know that,

cose θ – co θ =

16 – 9 = 576

**Question 7.**

**Question 8.Find the acute angle 0 such that 5tan2 0 + 3 = 9sec 0.Solution:**

**Question 9.Find sin θ such that 3cos θ + 4sin θ = 4.Solution:**

**Question 10.If cosec θ + cot θ = 5, then evaluate sec θ.Solution:**

**Question 11.Solution:**

We know that,

[Note: The question has been modified.]

**Question 12.Find the Cartesian co-ordinates of points whose polar co-ordinates are:i. (3, 90°) ii. (1, 180°)Solution:**

i. (r, θ) = (3, 90°)

Using x = r cos θ and y = r sin θ, where (x, y) are the required cartesian co-ordinates, we get

x = 3cos 90° and y = 3sin 90°

∴ x = 3(0) = 0 and y = 3(1) = 3

∴ the required cartesian co-ordinates are (0, 3).

ii. (r, θ) = (1, 180°)

Using x = r cos θ and y = r sin θ, where (x, y) are the required cartesian co-ordinates, we get

x = 1(cos 180°) and y = 1(sin 180°)

∴ x = -1 and y = 0

∴ the required cartesian co-ordinates are (-1, 0).

**Question 13.Find the polar co-ordinates of points whose Cartesian co-ordinates are:**

**Question 14.**

dhana work.txt

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