   Question Answers

# If $\sin {15^ \circ } = \cos \left( {n \times {{15}^ \circ }} \right)$, then n=______.A. 1B. 2C. 5D. 0  Hint: When two lines one real axis and the other imaginary axis passes perpendicular through a circle, the circle is divided into four quadrants. Into Quadrant I where both x and y axis are positive, Quadrant II here x axis is negative and y axis is positive, Quadrant III here both the x axis and y axis are negative and in Quadrant IV x-axis is positive and y-axis is negative.
In case of the trigonometric functions in Quadrant I all the functions are positive, in Quadrant II Sin and Cosec functions are positive and other functions are negative, in Quadrant III tan and cot functions are positive and other are negative and in the case of Quadrant IV Cos and Sec functions are positive and other being negative. In this question for the given equation we will cofunction identities of the trigonometric function.

Complete step by step solution: $\sin {15^ \circ } = \cos \left( {n \times {{15}^ \circ }} \right)$
By the rule of cofunction identity,$\sin \theta = \cos \left( {{{90}^ \circ } - \theta } \right)$
We can write as:
$\sin \theta = \cos \left( {{{90}^ \circ } - \theta } \right) \\ \sin {15^ \circ } = \cos \left( {{{90}^ \circ } - {{15}^ \circ }} \right) \\ = \cos \left( {{{75}^ \circ }} \right) \\ \\$
We can also write, $\cos \left( {{{75}^ \circ }} \right) = \cos \left( {5 \times {{15}^ \circ }} \right) = \cos \left( {n \times {{15}^ \circ }} \right)$
Hence, the value of n=5,
Where $\sin {15^ \circ }$and $\cos \left( {{{75}^ \circ }} \right)$both lie in the Quadrant I where all the trigonometric functions are positive. Quadrant I lie in the range of $0 - {90^ \circ }$.

Note: The co-function identities show the relationship between the sin, cos, tan, cosine, sec and cot function. The value of the trigonometric function for an angle is equal to the value of the co-function of the complement.
Table of 15 - Multiplication Table of 15  Sin Cos Formula  TS Grewal Solution for Class 11 Accountancy Chapter 15  DK Goel Solutions Class 11 Accountancy Chapter 15  The P-Block Elements  Difference Between Left and Right Ventricle  CBSE Class 9 Maths Chapter 15 - Probability Formulas  Difference Between Left Kidney and Right Kidney  CBSE Class 10 Maths Chapter 15 - Probability Formula  CBSE Class 8 Maths Chapter 15 - Introduction to Graphs Formulas  Important Questions for CBSE Class 11 Maths Chapter 15 - Statistics  NCERT Books Free Download for Class 11 Maths Chapter 15 - Statistics  Important Questions for CBSE Class 11 Biology Chapter 15 - Plant Growth and Development  Important Questions for CBSE Class 11 Physics Chapter 15 - Waves  Important Questions for CBSE Class 8 Maths Chapter 15 - Introduction to Graphs  Important Questions for CBSE Class 10 Maths Chapter 15 - Probability  Important Questions for CBSE Class 9 Maths Chapter 15 - Probability  NCERT Books Free Download for Class 11 Physics Chapter 15 - Waves  Important Questions for CBSE Class 11 Hindi Antra Chapter 15 Poem Jaag Tujhko Dur Jana Sab Ankho Ki Aansu Ujle  NCERT Books Free Download for Class 11 Biology Chapter 15 - Plant Growth and Development  Maths Question Paper for CBSE Class 12 - 2016 Set 1 N  Chemistry Question Paper for CBSE Class 12 - 2016 Set 1 N  Previous Year Question Paper for CBSE Class 12 Physics - 2016 Set 1 N  CBSE Class 12 Maths Question Paper 2020  CBSE Class 10 Maths Question Paper 2020  CBSE Class 10 Maths Question Paper 2017  Maths Question Paper for CBSE Class 10 - 2011  Maths Question Paper for CBSE Class 10 - 2008  Maths Question Paper for CBSE Class 10 - 2012  Maths Question Paper for CBSE Class 10 - 2009  RD Sharma Class 11 Solutions Chapter 15 - Linear Inequations (Ex 15.6) Exercise 15.6  RD Sharma Class 11 Solutions Chapter 15 - Linear Inequations (Ex 15.1) Exercise 15.1  NCERT Solutions for Class 11 Maths Chapter 15 Statistics (Ex 15.3) Exercise 15.3  RD Sharma Class 11 Solutions Chapter 15 - Linear Inequations (Ex 15.3) Exercise 15.3  RD Sharma Class 11 Solutions Chapter 15 - Linear Inequations (Ex 15.2) Exercise 15.2  RD Sharma Class 11 Solutions Chapter 15 - Linear Inequations (Ex 15.4) Exercise 15.4  RD Sharma Class 11 Solutions Chapter 15 - Linear Inequations (Ex 15.5) Exercise 15.5  NCERT Solutions for Class 11 Maths Chapter 15 Statistics (Ex 15.2) Exercise 15.2  NCERT Solutions for Class 11 Maths Chapter 15 Statistics (Ex 15.1) Exercise 15.1  RS Aggarwal Solutions Class 7 Chapter-15 Properties of Triangles (Ex 15A) Exercise 15.1  