sin^{-1} left( frac{12}{13} right) - sin^{-1} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) ધારો કે $\alpha = \sin^{-1} \left( \frac{12}{13} \right)$ અને $\beta = \sin^{-1} \left( \frac{3}{5} \right)$.તેથી $\sin \alpha = \frac{12}{13} \im

Vedclass · Accepted Answer

$\frac{\pi}{2} - \sin^{-1} \left( \frac{56}{65} \right)$

Vedclass · Answer

(D) ધારો કે $\alpha = \sin^{-1} \left( \frac{12}{13} ight)$ અને $\beta = \sin^{-1} \left( \frac{3}{5} ight)$.તેથી $\sin \alpha = \frac{12}{13} \implies \cos \alpha = \sqrt{1 - \left( \frac{12}{13} ight)^2} = \frac{5}{13}$.અને $\sin \beta = \frac{3}{5} \implies \cos \beta = \sqrt{1 - \left( \frac{3}{5} ight)^2} = \frac{4}{5}$.સૂત્ર $\sin^{-1} x - \sin^{-1} y = \sin^{-1} (x \sqrt{1 - y^2} - y \sqrt{1 - x^2})$ નો ઉપયોગ કરતા:$\sin^{-1} \left( \frac{12}{13} ight) - \sin^{-1} \left( \frac{3}{5} ight) = \sin^{-1} \left( \frac{12}{13} 	imes \frac{4}{5} - \frac{3}{5} 	imes \frac{5}{13} ight)$$= \sin^{-1} \left( \frac{48}{65} - \frac{15}{65} ight) = \sin^{-1} \left( \frac{33}{65} ight)$.આપણે જાણીએ છીએ કે $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$,તેથી $\sin^{-1} \left( \frac{33}{65} ight) = \frac{\pi}{2} - \cos^{-1} \left( \frac{33}{65} ight)$.વૈકલ્પિક રીતે,$\cos^{-1} x = \sin^{-1} \sqrt{1 - x^2}$ નો ઉપયોગ કરતા,$\sin^{-1} \left( \frac{33}{65} ight) = \cos^{-1} \sqrt{1 - \left( \frac{33}{65} ight)^2} = \cos^{-1} \left( \frac{56}{65} ight) = \frac{\pi}{2} - \sin^{-1} \left( \frac{56}{65} ight)$.આમ,સાચો વિકલ્પ $D$ છે.

$\sin^{-1} \left( \frac{12}{13} \right) - \sin^{-1} \left( \frac{3}{5} \right)$ નું મૂલ્ય કેટલું થાય?

Similar Questions

$\sin ^{-1}\left(\frac{3}{5}\right)-\sin ^{-1}\left(\frac{8}{17}\right)=$ . . . . . .

જો $x \geq 1$ હોય,તો $2 \tan^{-1} x + \sin^{-1} (\frac{2x}{1+x^2})$ ની કિંમત શું થાય?

જો $x \in [-1/2, 1/2]$ માટે $y = 3 \sin^{-1}x + \sin^{-1}(3x - 4x^3)$ હોય, તો

$\tan^{-1}(-2) - \tan^{-1}(3)$ ની કિંમત શોધો.

$n \in N$ માટે,જો $\cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^{-1} n=\frac{\pi}{4}$ હોય,તો $n$ ની કિંમત ......... છે.

Vedclass Test Series

Exam Paper Generator

Online Exam Module