Question : The expression $( an heta+\cot heta)(\sec heta+ an heta)(1-\sin heta), 0^{\circ}

Question

Question : The expression $( an heta+\cot heta)(\sec heta+ an heta)(1-\sin heta), 0^{\circ}< heta<90^{\circ}$, is equal to:

Option 1: $\sec heta$

Option 2: $\operatorname{cosec} heta$

Option 3: $\cot heta$

Option 4: $\sin heta$

Team Careers360 · Accepted Answer

Correct Answer: $\operatorname{cosec} heta$

Solution : Using the trigonometric identities $ an heta = \frac{\sin heta}{\cos heta}$, $\cot heta = \frac{\cos heta}{\sin heta}$, $\sec heta = \frac{1}{\cos heta}$, and $1 - \sin^2 heta = \cos^2 heta$.
Substituting these identities into the expression,
$=(\frac{\sin heta}{\cos heta} + \frac{\cos heta}{\sin heta})(\frac{1}{\cos heta} + \frac{\sin heta}{\cos heta})(1-\sin heta)$
Simplifying this expression,
$=(\frac{\sin^2 heta + \cos^2 heta}{\sin heta \cos heta})(\frac{\sin heta + 1}{\cos heta})(1-\sin heta)$
Using the identity $\sin^2 heta + \cos^2 heta = 1$,
$=(\frac{1}{\sin heta \cos heta})(\frac{(1-\sin ^2 heta)}{\cos heta})$
$=(\frac{1}{\sin heta \cos heta})(\frac{(cos ^2 heta)}{\cos heta})$
$=\frac{1}{\sin heta} $
$=\operatorname{cosec} heta$
Hence, the correct answer is $\operatorname{cosec} heta$.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Online Courses

Products

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Student Visas

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : The expression (tan⁡θ+cot⁡θ)(sec⁡θ+tan⁡θ)(1−sin⁡θ),0∘<θ<90∘, is equal to:Option 1: sec⁡θOption 2: cosecθOption 3: cot⁡θOption 4: sin⁡θ

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : The expression $(\tan θ + \cot θ) (\sec θ + \tan θ) (1 - \sin θ), 0^{\circ} < θ < 90^{\circ}$ , is equal to:
Option 1: $\sec θ$
Option 2: $cosec θ$
Option 3: $\cot θ$
Option 4: $\sin θ$