Q. 2 B

# For the principal

Let,

sin–1 = y

sin y =

–sin y =

–sin

As we know sin(–θ) = –sinθ

–sin = sin

The range of principal value of sin–1 is and sin

Therefore, the principal value of sin–1 is ….(1)

Let us assume 2tan = θ

We know tan

2tan = 2

2tan =

The question converts to sec–1

Now,

Let sec–1 = z

sec z =

= sec

The range of principal value of sec–1is [0, π]–{}

and sec

Therefore, the principal value of sec–1(2tan) is …..(2)

Sin–1 – 2sec–1(2tan)

= (from (1) and (2))

=

= –π

Therefore, the value of Sin–1 – 2sec–1(2tan) is –π.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

State True or FalMathematics - Exemplar

State True or FalMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Find the principaRD Sharma - Volume 1

State True or FalMathematics - Exemplar

State True or FalMathematics - Exemplar