Find the value of (1−cos⁡2θ)(cot⁡2θ+1)−1(1 - \cos^2 \theta)(\cot^2 \theta + 1)

Correct option is B

Given:

$(1 - \cos^2 \theta)(\cot^2 \theta + 1) - 1$

Used identity:

$\cos^2 \theta + \sin^2 \theta = 1$ 

Solution:

$= (1 - \cos^2 \theta)(\cot^2 \theta + 1) - 1 \\\ \\= \sin^2 \theta \times \left(\frac{\cos^2 \theta}{\sin^2 \theta} + 1\right) - 1 \\ \ \\= \sin^2 \theta \times \left(\frac{\cos^2 \theta + \sin^2 \theta}{\sin^2 \theta}\right) - 1 \\\ \\= \sin^2 \theta \times \left(\frac{1}{\sin^2 \theta}\right) - 1 \\\ \\= 1 - 1 \\\ \\= 0$

Free Tests

Free

Must Attempt

CBT-1 Full Mock Test 1

English

100 Questions
100 Marks
90 Mins

English

Free

Must Attempt

RRB NTPC Graduate Level PYP (Held on 5 Jun 2025 S1)

English

100 Questions
100 Marks
90 Mins

English

Free

Must Attempt

CBT-1 General Awareness Section Test 1

English

40 Questions
30 Marks
25 Mins

English

Find the value of $(1 - \cos^2 \theta)(\cot^2 \theta + 1) - 1$ ?

$\sec^2\theta$

0

2

-2

Correct option is B

Free Tests

CBT-1 Full Mock Test 1

RRB NTPC Graduate Level PYP (Held on 5 Jun 2025 S1)

CBT-1 General Awareness Section Test 1

Similar Questions

Access ‘RRB JE CBT-I’ Mock Tests with

Access ‘RRB JE CBT-I’ Mock Tests with

Discover Our Other Platforms

Find the value of (1−cos⁡2θ)(cot⁡2θ+1)−1(1 - \cos^2 \theta)(\cot^2 \theta + 1) - 1(1−cos2θ)(cot2θ+1)−1 ? ​

​sec⁡2θ\sec^2\thetasec2θ​​

0

2

-2

Correct option is B

Free Tests

CBT-1 Full Mock Test 1

RRB NTPC Graduate Level PYP (Held on 5 Jun 2025 S1)

CBT-1 General Awareness Section Test 1

Similar Questions

Access ‘RRB JE CBT-I’ Mock Tests with

Access ‘RRB JE CBT-I’ Mock Tests with

Find the value of $(1 - \cos^2 \theta)(\cot^2 \theta + 1) - 1$ ?

$\sec^2\theta$