Evaluate: ^ -1 (-7 25 ) - Vidyadip

Question

Evaluate:
$\tan\Big\{\cos^{-1}\Big(-\frac{7}{25}\Big)\Big\}$

✓

Answer

$\tan\Big\{\cos^{-1}\Big(-\frac{7}{25}\Big)\Big\}$
$=\tan\Big\{\cos^{-1}\Big(\pi-\frac{7}{25}\Big)\Big\}$
$=-\tan\Big\{\cos^{-1}\Big(\frac{7}{25}\Big)\Big\}$
$=-\tan\begin{Bmatrix}\tan^{-1}\begin{bmatrix}\frac{\sqrt{1-\Big(\frac{7}{25}\Big)^3}}{\frac{7}{25}}\end{bmatrix}\end{Bmatrix}$
$=-\tan\Big\{\tan\frac{24}{7}\Big\}$
$=-\frac{24}{7}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the value of $\lambda,$ non-zero scalar, if $\lambda\begin{bmatrix}1&0&2\\3&4&5\end{bmatrix}+2\begin{bmatrix}1&2&3\\-1&-3&2\end{bmatrix}=\begin{bmatrix}4&4&10\\4&2&14\end{bmatrix}$

Write a value of $\int\cos^4\text{x }\sin\text{x}\text{ dx}$

Write the identity relation on set A = {a, b, c}.

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:

₹ 50
₹ 20
₹ 40

The number of attempts made in three villages X, Y and Z are given below:

	(i)	(ii)	(iii)
X	400	300	100
Y	300	250	75
Z	500	400	150

Find the total cost incurred by the organisation for three villages separately, using matrices.

Evaluate $\int_0^\pi \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x$.

An unbiased dice is thrown twice. Let the event E be 'odd number on the first throw' and F the event 'odd number on the second throw'. Check the independence of events E and F .

Compute the indicated products:
$\begin{bmatrix}1&-2\\2&3\end{bmatrix}\begin{bmatrix}1&2&3\\-3&2&-1\end{bmatrix}$

Let * be a binary operation on the set Q of rational numbers as follows:
a * b = a – b

If $\text{A}=\begin{bmatrix}\cos\text{x}&-\sin\text{x}\\\sin\text{x}&\cos\text{x}\end{bmatrix},$ find AA^T.

If two events A and B are such that $\text{P}(\overline{\text{A}})=0.3,\text{P(B)}=0.4$ and $\text{P}(\text{A}\cap\overline{\text{B}})=0.5$ find $\text{P}\Big(\frac{\text{B}}{\overline{\text{A}}\cap\overline{\text{B}}}\Big).$