Pythagorean Identities MCQ Quiz in मल्याळम - Objective Question with Answer for Pythagorean Identities - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Given:

\sin A \sin B

Formula Used:

2 

Calculation:

We know that:

2 

Therefore,

sin A sin B  = }

Thus, the correct answer is option 4.

Given:

Sec θ + 1/cos θ = 2

Concept used:

Calculation:

According to the question:

Sec θ + 1/cos θ = 2

Sec θ + sec θ  = 2

So, θ = 0° 

Now putting the value of θ in equation:

⇒ Sec⁵⁵ θ + 1/sec⁵⁵ θ 

⇒ Sec55 0° + 1/sec55 0°

⇒ 1 + 1 = 2

∴ The correct answer is 2.

Given:

Cos² θ = 3/4

Formula used:

Cos 30° = Sin 60° = √3/2

Calculation:

Cos2 θ = 3/4

⇒ cos θ = √(3/4) = √3/2

⇒ cos θ  = cos 30° 

⇒ θ = 30° 

sin (θ + 30°) =  sin (30° + 30°)

⇒ sin 60° = √3/2

∴ The correct answer is √3/2.

Given: 

If sec θ + tan θ = x, find sinθ.

Formulae Used:

(secθ + tanθ) (secθ - tanθ) = 1

Solution:

sec θ + tan θ = x   ---(1)

So, sec θ - tan θ = 1/x  ---(2)

Subtracting equation (2) from equation (1):

sec θ + tan θ - (sec θ - tan θ) = x - 1/x

⇒ sec θ + tan θ - sec θ + tan θ = (x² - 1)/x

⇒ 2 tan θ = (x² - 1)/x

⇒ tan θ = (x2 - 1)/2x

We know that tan θ = p/b

So, p = (x² - 1), b = 2x

h² = p² + b² = (x² - 1)² + (2x)²

⇒ h² = (x²)² + 1 - 2x² + 4x²

⇒ h2 = (x2)2 + 1 + 2x2

⇒ h2 = (x² + 1)²

⇒ h = (x² + 1)

So, sin θ = p/h = (x2 - 1) / (x2 + 1)

∴ The correct answer is option (3).

Formula used:

1 - sin² θ = cos² θ

Sec θ × cos θ = 1

Calculation:

Sec θ × √{1 - sin2 θ}

⇒ Sec θ × √{cos² θ} 

⇒ Sec θ × cos θ = 1

∴ The correct answer is 1. 

Given:

sec2A + tan2A = 3

Concept used:

sec2 α - tan2 α = 1

Calculation:

sec2A + tan2A = 3      ....(1)

sec2A - tan2A = 1      ....(2)

Solving (1) and (2) we get,

sec2A + tan2A - sec2A + tan2A = 3 - 1 = 2

2tan² A = 2

tan2 A = 1

So, tan A = √1 = 1

Now, cot A = 1/1 = 1

∴ The value of cot A is 1.

Given:

Formula Used:

Calculation:

⇒ 

⇒ 

⇒ 

⇒ 

The value of sec(t) is  .

Calculations:

We have,

cosec θ - cot θ = (1/sinθ) - (cosθ/sinθ) = (1 - cos θ)/sin θ

So,

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒  cot θ

∴ The correct answer is option (3).

Formula Used : 

Sin²θ + Cos²θ = 1

Calculation : 

⇒ (sin θ + cos θ)2 + (sin θ - cos θ)2

⇒ sin²θ + cos²θ + 2sinθcosθ + sin2θ + cos2θ - 2sinθcosθ 

⇒ 2(sin²θ + cos²θ)

⇒ 2

∴ The correct answer is 2.

Given:

The expression is:

Formula used:

We will use algebraic manipulation and trigonometric identities to simplify the given expression.

Calculations:

 Let x =  . Then, the expression becomes:

Simplify each term separately:

Now the expression becomes:

To combine the terms, we need a common denominator:

Simplify the numerator:

So, the expression becomes:

Substitute back  x = :

8. Using the identity  , the expression becomes:

 = 2

Thus, the simplified expression is: 2