Answer
Verified
497.7k+ views
Hint – Use the formula of \[{(a + b)^3}\] putting \[a = {\sin ^2}\theta \,\,\& \,\,b = {\cos ^2}\theta \].
We know \[{(a + b)^3} = {a^3} + {b^3} + 3{a^2}b + 3a{b^2}\,\,\,\,\,\,\,\,\,......(i)\]
Let \[a = {\sin ^2}\theta \,\,\& \,\,b = {\cos ^2}\theta \]
We also know \[{\sin ^2}\theta + {\cos ^2}\theta = 1\,\,\,\,\,\,\,...........(ii)\]
Then putting the value of \[a\& b\] in \[{\text{(}}i{\text{)}}\]
We get,
\[{({\sin ^2}\theta + {\cos ^2}\theta )^3} = {\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta ({\sin ^2}\theta + {\cos ^2}\theta )\]
\[{\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta (1) = 1\,\,\,\,\,\,\,({\text{from (}}ii{\text{)}})\]
\[{\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta = 1\,\,\,\,\,\,\,({\text{from (}}ii{\text{)}})\]
Hence the answer is \[C\].
Note – In these type of questions of trigonometry we have to use basic concepts like \[{\text{(}}{\sin ^2}\theta + {\cos ^2}\theta = 1)\] and we also used the general formula of \[{{\text{(a + b)}}^{3\;}}\], then we can
get the solution by solving the equation.
We know \[{(a + b)^3} = {a^3} + {b^3} + 3{a^2}b + 3a{b^2}\,\,\,\,\,\,\,\,\,......(i)\]
Let \[a = {\sin ^2}\theta \,\,\& \,\,b = {\cos ^2}\theta \]
We also know \[{\sin ^2}\theta + {\cos ^2}\theta = 1\,\,\,\,\,\,\,...........(ii)\]
Then putting the value of \[a\& b\] in \[{\text{(}}i{\text{)}}\]
We get,
\[{({\sin ^2}\theta + {\cos ^2}\theta )^3} = {\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta ({\sin ^2}\theta + {\cos ^2}\theta )\]
\[{\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta (1) = 1\,\,\,\,\,\,\,({\text{from (}}ii{\text{)}})\]
\[{\sin ^6}\theta + {\cos ^6}\theta + 3{\sin ^2}\theta {\cos ^2}\theta = 1\,\,\,\,\,\,\,({\text{from (}}ii{\text{)}})\]
Hence the answer is \[C\].
Note – In these type of questions of trigonometry we have to use basic concepts like \[{\text{(}}{\sin ^2}\theta + {\cos ^2}\theta = 1)\] and we also used the general formula of \[{{\text{(a + b)}}^{3\;}}\], then we can
get the solution by solving the equation.
Recently Updated Pages
Identify the feminine gender noun from the given sentence class 10 english CBSE
Your club organized a blood donation camp in your city class 10 english CBSE
Choose the correct meaning of the idiomphrase from class 10 english CBSE
Identify the neuter gender noun from the given sentence class 10 english CBSE
Choose the word which best expresses the meaning of class 10 english CBSE
Choose the word which is closest to the opposite in class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
10 examples of friction in our daily life
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What is pollution? How many types of pollution? Define it