Introduction to Trigonometry Test

Result

Introduction to Trigonometry Test - 3

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If xcotθ - ycosecθ = a and xcosecθ - ycotθ = b, then (y² - x²)² is equal to

A
2(a² - b²)²

B
(a - b)²

C
(a² + b²)²

D
(a² - b²)²

Solution

xcotθ – ycosecθ = a
Squaring both sides, we get

x²cot²θ + y²cosec²θ – 2.xy.cotθ.cosecθ = a² --- (1)
xcosecθ – ycotθ = b
Squaring both sides, we get

x²cosec²θ + y²cot²θ – 2.xy.cosecθ.cotθ = b² --- (2)
Subtracting (2) from (1), we get

x²cot²θ + y²cosec²θ – 2.xy.cotθ.cosecθ - (x²cosec²θ + y²cot²θ – 2.xy.cosecθ.cotθ) = a² - b²
x²cot²θ + y²cosec²θ - x²cosec²θ - y²cot²θ = a² - b²

cosec²θ(y² – x²) – cot²θ(y² – x²) = a²– b²
(y² – x²)(cosec²θ – cot²θ) = a² – b²
(y² – x²) = a² – b²

Squaring both sides,
(y² – x²)² = (a² - b²)²
Question 2
1 / -0

If tan A + cot A = 4, then what is the value of tan³ A + cot³ A?

A
52

B
64

C
48

D
72

Solution

According to the question,
(a + b)³ = a³ + b³ + 3ab (a + b)
∴ a³ + b³ = (a + b)³ - 3ab (a + b)

So, tan³ A + cot³ A = (tan A + cot A)³- 3 . tan A . cot A (tan A + cot A)
= (4)³ - 3 × 4
= 64 - 12 = 52