3,left[ {{{sin }^4},left( {frac{{3pi }}{2} - | vedclass

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

Question

(B) આપેલ પદાવલિ: $3\left[ {{{\sin }^4}\left( {\frac{{3\pi }}{2} - \alpha } \right) + {{\sin }^4}(3\pi + \alpha )} \right] - 2\left[ {{{\sin }^6}\left(

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) આપેલ પદાવલિ: $3\left[ {{{\sin }^4}\left( {\frac{{3\pi }}{2} - \alpha } \right) + {{\sin }^4}(3\pi + \alpha )} \right] - 2\left[ {{{\sin }^6}\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}(5\pi - \alpha )} \right]$ત્રિકોણમિતીય નિત્યસમનો ઉપયોગ કરતા:$\sin(\frac{3\pi}{2} - \alpha) = -\cos \alpha$,$\sin(3\pi + \alpha) = -\sin \alpha$$\sin(\frac{\pi}{2} + \alpha) = \cos \alpha$,$\sin(5\pi - \alpha) = \sin \alpha$આ કિંમતો મૂકતા:$= 3\left[ {(-\cos \alpha)^4 + (-\sin \alpha)^4} \right] - 2\left[ {(\cos \alpha)^6 + (\sin \alpha)^6} \right]$$= 3(\cos^4 \alpha + \sin^4 \alpha) - 2(\cos^6 \alpha + \sin^6 \alpha)$નિત્યસમ $a^2+b^2 = (a+b)^2 - 2ab$ અને $a^3+b^3 = (a+b)^3 - 3ab(a+b)$ નો ઉપયોગ કરતા:$= 3[(\cos^2 \alpha + \sin^2 \alpha)^2 - 2\sin^2 \alpha \cos^2 \alpha] - 2[(\cos^2 \alpha + \sin^2 \alpha)^3 - 3\sin^2 \alpha \cos^2 \alpha(\cos^2 \alpha + \sin^2 \alpha)]$કારણ કે $\sin^2 \alpha + \cos^2 \alpha = 1$:$= 3[1 - 2\sin^2 \alpha \cos^2 \alpha] - 2[1 - 3\sin^2 \alpha \cos^2 \alpha]$$= 3 - 6\sin^2 \alpha \cos^2 \alpha - 2 + 6\sin^2 \alpha \cos^2 \alpha$$= 3 - 2 = 1$

$3\,\left[ {{{\sin }^4}\,\left( {\frac{{3\pi }}{2} - \alpha } \right) + {{\sin }^4}\,(3\pi + \alpha )} \right] - 2\,\left[ {{{\sin }^6}\,\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}(5\pi - \alpha )} \right] = $

Similar Questions

$\cos A + \sin (270^\circ + A) - \sin (270^\circ - A) + \cos (180^\circ + A) = $

$\frac{\tan ^{2} \theta}{\sec \theta+1}-\sec \theta$ ની કિંમત શોધો.

જો $2y \cos \theta = x \sin \theta$ અને $2x \sec \theta - y \csc \theta = 3$ હોય,તો $x^2 + 4y^2 = $

જો $\tan \theta = \frac{a}{b}$ હોય,તો $\frac{{\sin \theta }}{{{{\cos }^8}\theta }} + \frac{{\cos \theta }}{{{{\sin }^8}\theta }} = $

જો $\cos \theta = \frac{x^{2}-y^{2}}{x^{2}+y^{2}}$ હોય,તો $\cot \theta$ ની કિંમત શોધો (જ્યાં $0^{\circ} \leq \theta \leq 90^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module