Trigonometric Function MCQ Quiz - Objective Question with Answer for Trigonometric Function - Download Free PDF

Calculation

Using L’hopital rule 

Hence option 3 is correct

Calculation:

We have to find the value of 

∴ Option 4 is correct.

Explanation:

=  Form]

=   (using L' hospital rule)

∴ Option (b) is correct.

Calculation

Using L’hopital rule 

Hence option 3 is correct

Calculation:

Given:

∴  = 1.414

Formula used:

Calculation:

Since, 1 - cos 2θ = sin²θ

⇒ 

⇒ 

∴   = √2

Concept:

Trigonometry formulas:

1 - cos 2x = 2sin² x

1 + cos 2x = 2cos² x

Calculation:

Here, we have to find the value of the limit 

As we know, 1 - cos 2x = 2sin2 x

= 

= 2 × 

= 2 × 1 × 1

= 2

Concept:

sin(a) - sin(b) = 2 cos() sin()......(1)

.........(2)

Explanation:

We are given   

 (Using equation 1)

⇒ 2 cos (2) × 1 (Using equation 2) 

⇒ 2 cos 2

Calculation:

We have,

      (∵ tan x = sin x/cos x)

      (∵ sin² x = 1 - cos² x)

 is the correct limit.

Concept:

Calculation:

Here, we have to find the value of the limit 

= 

= 

= 

= 2

Concept:

Calculation:

Given: 

We know that 180° = π Radian

∴ 1° = π /360 ⇒ x° = πx/180 

= 

∴ Option 2 is correct.

Concept:

Formula: 

L-Hospital Rule: Let f(x) and g(x) be two functions

Suppose that we have one of the following cases,

I. 

II. 

Then we can apply L-Hospital Rule:

Note: We have to differentiate both the numerator and denominator with respect to x unless and until  where l is a finite value.

Calculation:

We have to find the value of 

                      Form of limit is (0/0)

Applying L-Hospital rule, we get

= 1

Concept:

Formula: 

L-Hospital Rule: Let f(x) and g(x) be two functions

Suppose that we have one of the following cases,

I. 

II. 

Then we can apply L-Hospital Rule:

Note: We have to differentiate both the numerator and denominator with respect to x unless and until  where l is a finite value.

Calculation:

We have to find the value of 

                      Form of limit is (0/0)

Applying L-Hospital rule, we get

= 0

Concept:

L’ Hospital’s rule:

If  then we have to differentiate both the numerator and denominator with respect to x unless and until  where l is a finite value.

Calculation:

Given:

By applying L hospital’s rule we get

Calculation:

We have to find the value of 

∴ Option 4 is correct.