Find the principal value of egin{align | Class 12 Mathematics Chapter Inverse Trigonometric Functions, Inverse Trigonometric Functions NCERT Solutions

Question: Find the principal value of \begin{align} cos^{-1}\left(\frac{1}{2}\right) + 2sin^{-1}\left(\frac{1}{2}\right)\end{align}
Answer:

\begin{align} Let \;\;cos^{-1}\left(\frac{1}{2}\right) =x. \;\;Then,\;\; cos x = \frac{1}{2} = cos\left(\frac{\pi}{3}\right).\end{align}

\begin{align}  \therefore cos^{-1}\left(\frac{1}{2}\right)  = \frac{\pi}{3}\end{align}

\begin{align} Let \;\; sin^{-1}\left(\frac{1}{2}\right)=y. \;\;Then,\;\; sin y = \frac{1}{2} = sin\left(\frac{\pi}{6}\right).\end{align}

\begin{align}  \therefore sin^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}\end{align}

\begin{align} \therefore cos^{-1}\left(\frac{1}{2}\right) + 2sin^{-1}\left(\frac{1}{2}\right)\end{align}

\begin{align} =\frac{\pi}{3} + \frac{2\pi}{6} = \frac{\pi}{3} + \frac{\pi}{3} = \frac{2\pi}{3}\end{align}


Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

  • Read the question carefully and focus on the core concept being asked.
  • Reference examples and data from the chapter when answering questions about Inverse Trigonometric Functions.
  • Review previous year question papers to get an idea of how such questions may be framed in exams.
  • Practice answering questions within the time limit to improve your speed and accuracy.
  • Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Notice: Undefined index: quesId in /var/www/html/ss_beta/saralstudy/ss_new/web/template/common/comment_section.php on line 3

Comments

Comment(s) on this Question

Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 12: Find the principal value of egin{align} cos^{-1}left(frac{1}{2} ight) + 2sin^{-1}left(frac{1}....