Yarim burchak formulalari mavzusidan test savollari

Hisoblang. sin105^\circ +sin75^\circ

Agar cos2\alpha =\frac{1}{2} bo‘lsa, \cos ^{2}\alpha ni hisoblang.

\sin \frac{\pi }{12} ni hisoblang.

Agar cos\alpha =-\frac{1}{2} va \pi<\alpha<\frac{3\pi }{2} bo‘lsa, \sin (\frac{\pi }{2}+\frac{\alpha }{2}) ni toping.

Agar 0<a<\frac{\pi }{2} va cos\alpha =\frac{1}{2}\sqrt{2+\sqrt{2}} bo‘lsa, \alpha ni toping.

Hisoblang. \sin (202^\circ 30^{'})

Hisoblang: \sin112.5^\circ

Qaysi \alpha o‘tkir burchak uchun cos\alpha =\frac{1}{2}\sqrt{2+\sqrt{3}} tenglik to‘g‘ri?

Hisoblang. \cos \frac{\pi }{12}.

Hisoblang. 8cos30^\circ +tg^{2}15^\circ

Agar cos\alpha =\frac{1}{2} va \frac{3\pi }{2}<\alpha<2\pi bo‘lsa, \sin (\pi -\frac{\alpha }{2}) ni toping.

Hisoblang. \cos \frac{5\pi }{12}

Soddalashtiring. 4ctg30^\circ +tg^{2}15^\circ

Hisoblang. \sin \frac{5\pi }{12}.

Agar cos\alpha =-\frac{1}{2} va \pi<\alpha<1.5\pi bo‘lsa, \cos (\frac{\pi }{2}+\frac{\alpha }{2})ni toping.

Agar cos\alpha =\frac{7}{18}, 0<\alpha<\frac{\pi }{2} bo‘lsa, 6cos\frac{\alpha }{2} ni toping.

Agar 450^\circ<\alpha<540^\circ va ctg\alpha =-\frac{7}{24} bo‘lsa, \cos \frac{\alpha }{2} ni hisoblang.

Soddalashtiring. \frac{\cos ^{2}x+cosx}{2\cos ^{2}\frac{x}{2}}+1

Soddalashtiring. \sqrt{\frac{1+sin(\frac{3\pi }{2}+\alpha )}{1+sin(\frac{\pi }{2}+\alpha )}}

Soddalashtiring. \frac{\sin ^{4}\alpha +2cos\alpha \cdot sin\alpha -\cos ^{4}\alpha }{2\cos ^{2}\alpha -1}

Agar sin\alpha =-0, 8 va \alpha \in (\pi ;\frac{3\pi }{2}) bo‘lsa, tg\frac{\alpha }{2} ni aniqlang.

Hisoblang. \sin ^{4}15^\circ +\cos ^{4}15^\circ

Hisoblang. \cos ^{2}5+\cos ^{2}1-cos6\cdot cos4

\cos ^{2}73^\circ + \cos ^{2}47^\circ + cos73^\circ \cdot cos47^\circ ni soddalashtiring.

8\sin ^{2}\frac{7\pi }{8}\cdot \cos ^{2}\frac{9\pi }{8} ni hisoblang.

Agar \cos (\pi -4\alpha )=-\frac{1}{3} bo‘lsa, \cos ^{4}(\frac{3\pi }{2}-2\alpha )ni hisoblang.

Agar \sin (\alpha +\beta )=\frac{4}{5}, \sin(\alpha -\beta )=\frac{5}{13} va 0<\beta<\alpha <\frac{\pi }{4} bo‘lsa, \sin\alpha +\sin\beta ning qiymatini hisoblang.

\frac{\cos ^{2}68^\circ -\cos ^{2}38^\circ }{sin106^\circ } ni hisoblang.

\cos ^{8}165^\circ -\sin ^{8}165^\circ ni hisoblang.

\frac{2\cos ^{2}(45^\circ -\frac{\alpha }{2})}{cos\alpha } ni soddalashtiring.