COMEDK · Maths · 23. Inverse Trigonometric Functions

If \(\cos ^{-1} p+\cos ^{-1} q+\cos ^{-1} r=\pi\), then \(p^{2}+q^{2}+r^{2}+2 p q r\) is equal to

A \(3\)
B \(1\)
C \(2\)
D \(-1\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1\)

Step-by-step Solution

Detailed explanation

We have,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If \(y=\tan ^{-1}\left(\frac{1}{1+x+x^{2}}\right)+\tan ^{-1}\left(\frac{1}{x^{2}+3 x+3}\right)\) \(+\tan ^{-1}\left(\frac{1}{x^{2}+5 x+7}\right)+\ldots+\) upto \(n\) terms then \(\frac{d y}{d x}\) at \(x=0\) and \(n=1\) is equal to

COMEDK 2012 Easy
The value of \(\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) is

COMEDK 2017 Medium
The probability distribution of a discrete random variable X is given as

X 1 2 4 2A 3A 5A
P(X) \(\dfrac{1}{2}\) \(\dfrac{1}{5}\) \(\dfrac{3}{25}\) K \(\dfrac{1}{25}\) \(\dfrac{1}{25}\)

\(\text { Then the value of } A \text { if } E(X)=2.94 \text { is }\)

COMEDK 2023 Medium
\(\lim _{x \rightarrow 0} \dfrac{\sqrt{1-\cos 2 x}}{x \sqrt{2}}\)

COMEDK 2025 Medium
If \((p \wedge \sim r) \rightarrow(\sim p \vee q)\) is false, then the truth values of \(p, q\) and \(r\) are respectively

COMEDK 2016 Easy
\(\int_0^{\pi/2} \dfrac{3\sin x + 4\cos x}{\sin x + \cos x}\, dx =\)

COMEDK 2026 Medium

X	1	2	4	2A	3A	5A
P(X)	\(\dfrac{1}{2}\)	\(\dfrac{1}{5}\)	\(\dfrac{3}{25}\)	K	\(\dfrac{1}{25}\)	\(\dfrac{1}{25}\)

Explore more questions on app

From COMEDK

Choose the correct statement.

COMEDK 2025 Medium
A motor cyclist starts from the top of an inclined plane of height h to go around a globe of death trap of radius r. The ratio of minimum height 'h' of the inclined plane to the radius 'r' of the death globe in order to go around the death globe successfully is

COMEDK 2026 Medium
The smallest positive integer \(n\) for which \((1+i)^{2 n}=(1-i)^{2 n}\) is

COMEDK 2013 Easy
A straight lines meets the coordinates axes at \(A\) and \(B\), so that the centroid of the \(\triangle O A B\) is \((1,2)\). Then, the equation of the line \(A B\) is

COMEDK 2015 Easy
If the line \(p x+q y=0\) coincides with one of the lines given by \(a x^{2}+2 h x y+b y^{2}=0\), then

COMEDK 2018 Easy
Given the matrices \(A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 2 \end{bmatrix}\) and \(B = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 1 & 2 \\ 0 & 2 & 1 \end{bmatrix}\), then the minor \(M_{23}\) of the matrix \((A B^{-1})^{-1}\) is:

COMEDK 2026 Medium

Explore more questions on app