Trigonometriyaning asosiy ayniyatlari mavzusidan test savollari

Agar \sin \alpha =\frac{3}{5 } va \frac{\pi }{2}<\alpha<\pi bo‘lsa, tg\alphani toping.

Agar \alpha \in (\frac{\pi }{2};\pi ) va \sin \alpha =\frac{1}{4} bo‘lsa, ctg\alpha ni hisoblang.

Agar 0<\alpha<\frac{\pi}{2} va tg{\alpha}=2 bo‘lsa, cos{\alpha} ni toping.

Agar tg\alpha =3 bo‘lsa, \frac{3\sin \alpha }{5\sin ^3\alpha +10cos^3\alpha } ning qiymati qanchaga teng bo‘ladi?

Ifodani soddalashtiring:
\sin^2\alpha +\cos ^2\alpha +ctg^2\alpha

Agar \sqrt{1-\cos ^2x}-\sqrt{1+\sin ^{2}x}=k bo‘lsa, \sqrt{1-\cos ^2x}+\sqrt{1+\sin ^{2}x} ni toping.

Agar tg\alpha +ctg\alpha =p bo‘lsa, tg^3\alpha +ctg^3\alpha ni p orqali ifodalang.

Agar tg\alpha +ctg\alpha =a (a>0) bo‘lsa, \sqrt{tg\alpha }+\sqrt{ctg\alpha } ni qiymati qanchaga teng bo‘ladi?

Agar \sin \alpha +\cos\alpha =a bo‘lsa, |\sin \alpha -\cos\alpha | ni a orqali ifodalang.

Agar tg\alpha +ctg\alpha =p bo‘lsa, tg^2\alpha +ctg^2\alpha ni p orqali ifodalang.

Soddalashtiring:
\sin^2\alpha + \sin^2\beta - \sin^2\alpha \cdot \sin^2\beta +\cos^2\alpha \cdot \cos^2\beta

tgx ni hisoblang. \frac{2\sin x-\cos x}{2\cos x+\sin x}=3

Soddalashtiring:

\sin ^{6}\alpha +\cos ^{6}\alpha +3\sin ^{2}\alpha \cdot \cos ^{2}\alpha

Soddalashtiring:

\sin ^{2}x+\cos ^{2}x+tg^{2}x

Agar tg\alpha =\frac{4}{5} bo‘lsa, \frac{sin\alpha +cos\alpha }{sin\alpha -cos\alpha } nimaga teng.

Agar ctg\alpha =\sqrt{3} bo‘lsa, \frac{9}{\sin ^{4}\alpha +\cos ^{4}\alpha } ni hisoblang.

Soddalashtiring:
(ctg\alpha -\cos\alpha )\cdot (\frac{\sin^2\alpha }{\cos\alpha }+tg\alpha )

Soddalashtiring:

\frac{1-\sin ^{4}\alpha -\cos ^{4}\alpha }{\cos ^{4}\alpha }

Soddalashtiring.

\frac{\sin^2\alpha -\cos^{2}\alpha +\cos ^{4}\alpha }{\cos ^{2}\alpha -\sin^{2}\alpha +\sin ^{4}\alpha }

Soddalashtiring.

\frac{3\sin^2\alpha +\cos ^{4}\alpha }{1+\sin^{2}\alpha +\sin ^{4}\alpha }

Soddalashtiring.

\frac{1+\cos^2\alpha +\cos ^{4}\alpha }{3\cos^2\alpha +\sin ^{4}\alpha }

Agar sin\alpha =\frac{\sqrt{3}}{2} va \frac{\pi }{2}<\alpha <\pi bo‘lsa, \frac{\vert -1+cos\alpha \vert +2cos\alpha }{|\frac{tg\alpha }{\sqrt{3}}-0.5|} ni hisoblang

Agar ctg\alpha =\frac{13}{4} bo‘lsa, \frac{2cos\alpha +sin\alpha }{cos\alpha -2sin\alpha } kasrning qiymatini toping.

Hisoblang:
[\frac{\log _{\pi }2\pi }{tg^2\frac{\pi }{2}+1}]^{\sin^2\frac{\pi }{5}+\cos^2\frac{\pi }{5}-1}

Ifodani soddalashtiring:
\frac{\cos^2\alpha -ctg^2\alpha }{tg^2\alpha -\sin^2\alpha }

Agar sinx+cosx=0.5 bo‘lsa, 16(sin^{3}x+cos^3x) ni toping.

Agar tg\alpha =-\frac{3}{4} va \frac{\pi }{2}<\alpha<\pi bo‘lsa, \sin\alpha-\cos\alpha ning qiymatini toping.

Agar cos\alpha =\frac{\sqrt{3}}{2} bo‘lsa, \frac{1-sin^{2}\alpha +cos^2\alpha \cdot sin\alpha }{1+sin\alpha } ifodaning qiymatini toping.

(tgx+ctgx)^{2}-(tgx-ctgx)^2 ni soddalashtiring.

Agar \frac{2\sin \alpha +3\cos \alpha }{5\sin \alpha -\cos \alpha } bo‘lsa, ctg\alpha =-2 ning qiymatini hisoblang.