
Simplify the following algebraic term:
$
\left( {1 + {{\tan }^2}\theta } \right).{\sin ^2}\theta = \\
A.{\text{ }}{\sin ^2}\theta \\
B.{\text{ }}{\cos ^2}\theta \\
C.{\text{ }}{\tan ^2}\theta \\
D.{\text{ }}{\cot ^2}\theta \\
$
Answer
552.6k+ views
Hint- For solving, use simple trigonometric identities and formulas.
Since we know that ${\text{se}}{{\text{c}}^2}\theta - {\tan ^2}\theta = 1$
$ \Rightarrow {\text{se}}{{\text{c}}^2}\theta = 1 + {\tan ^2}\theta $
Substituting the above equation in the give question,
Now the question becomes$\left[ {{\text{se}}{{\text{c}}^2}\theta } \right].{\sin ^2}\theta $
Further simplifying the trigonometric terms
$
\Rightarrow {\left[ {\sec \theta .\sin \theta } \right]^2} \\
\Rightarrow {\left[ {\dfrac{1}{{\cos \theta }}.\sin \theta } \right]^2} \\
\Rightarrow {\left[ {\tan \theta } \right]^2}\because \dfrac{{\sin \theta }}{{\cos \theta }} = \tan \theta \\
\Rightarrow {\tan ^2}\theta \\
$
Hence, the correct option is $C$
Note- Use Simple trigonometric formulas which are mentioned above along with the solution. These formulas must be remembered. Always try to reduce the equation by the use of trigonometric identities which further reduces the equation.
Since we know that ${\text{se}}{{\text{c}}^2}\theta - {\tan ^2}\theta = 1$
$ \Rightarrow {\text{se}}{{\text{c}}^2}\theta = 1 + {\tan ^2}\theta $
Substituting the above equation in the give question,
Now the question becomes$\left[ {{\text{se}}{{\text{c}}^2}\theta } \right].{\sin ^2}\theta $
Further simplifying the trigonometric terms
$
\Rightarrow {\left[ {\sec \theta .\sin \theta } \right]^2} \\
\Rightarrow {\left[ {\dfrac{1}{{\cos \theta }}.\sin \theta } \right]^2} \\
\Rightarrow {\left[ {\tan \theta } \right]^2}\because \dfrac{{\sin \theta }}{{\cos \theta }} = \tan \theta \\
\Rightarrow {\tan ^2}\theta \\
$
Hence, the correct option is $C$
Note- Use Simple trigonometric formulas which are mentioned above along with the solution. These formulas must be remembered. Always try to reduce the equation by the use of trigonometric identities which further reduces the equation.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write examples of herbivores carnivores and omnivo class 10 biology CBSE

When and how did Canada eventually gain its independence class 10 social science CBSE
