Question

Refer the attachment for the questions.
Solve any 3. ​

Answer 1

Step-by-step explanation:

(iv)

Given Sec²θ + cosec²θ:

⇒ (1/cos²θ) + (1/sin²θ)

⇒ (sin²θ + cos²θ)/(cos²θ * sin²θ)

⇒ (1/cos²θ * sin²θ)

⇒ (1/cos²θ) * (1/sin²θ)

⇒ sec²θ * cosec²θ.

(v)

Given points are (4,-5) and (-1,-2).

∴ Equation of a line passing through (x₁,y₁) and (x₂,y₂) is:

⇒ (y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

⇒ (y + 5)/(-2 + 5) = (x - 4)/(-1 - 4)

⇒ (y + 5)/(3) = (x - 4)/(-5)

⇒ -5(y + 5) = 3(x - 4)

⇒ -5y - 25 = 3x - 12

⇒ 3x + 5y = -13

(or)

⇒ y = -(3/5)x - 13/5.

(iii)

Explained in the attachment.

Hope it helps!

Answer 2

Answer:

(i) In the triangle PQR:

sin 30 = 1/2 = QR/PQ

=> 1/2 = QR/12

=> QR = 6 cm

cos 30 = (_/3)/2 = PR/PQ

=> PR = 6_/3 cm

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(iv) Out the value of sec^2 Ø and cosec^2 Ø as:

sec^2 Ø = 1/cos^2 Ø

cosec^2 Ø = 1/sin^2 Ø

=> 1/cos^2 Ø + 1/sin^2 Ø = (sin^2 Ø + cos^2 Ø)/sin^2 Ø cos^2 Ø

=> 1/sin^2 Ø cos^2 Ø

[°.° sin^2 A + cos^2 A = 1]

=> sec^2 Ø cosec^2 Ø

Put back the values of sec^2 Ø and cosec^2 Ø, which we changed in the beginning.

(iii) in the attachment.

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Hope it Helps :D

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