Ikkilangan burchak formulalari mavzusidan test savollari

Soddalashtiring. \frac{\sin 3\alpha }{sin\alpha }- \frac{cos3a}{cos\alpha }

Hisoblang. \sin \frac{\pi }{16}\cdot \cos^3\frac{\pi }{16}-\sin^3\frac{\pi }{16}\cdot \cos \frac{\pi }{16}

Soddalashtiring. \frac{\sin (\pi -2\alpha )}{1-\sin (\frac{\pi }{2}-2\alpha )}

Agar cos\alpha =\frac{1}{5} bo‘lsa, \frac{2sin\alpha +\sin 2\alpha }{2sin\alpha -\sin 2\alpha } ni hisoblang.

Agar tg\alpha = -\frac{1}{4} bo‘lsa, \frac{2\cos ^{2}\alpha -\sin 2\alpha }{2\sin^2\alpha -\sin 2\alpha } ni hisoblang.

Hisoblang. tg 15^\circ - ctg15^\circ

Agar \alpha = 15^\circ bo‘lsa, (1 + \cos 2\alpha )tg\alpha ning qiymatini \frac{1}{8} bilan solishtiring.

Agar tg\alpha = \frac{1}{2} bo‘lsa, tg2\alpha ni toping.

Hisoblang. tg22.5^\circ+tg^{-1}22.5^\circ

Agar \sin \frac{\alpha }{2}+\cos \frac{\alpha }{2}=-\frac{1}{2} va \frac{3\pi }{2}

Hisoblang. \cos92^\circ\cdot \cos 2^\circ+0.5\cdot \sin 4^\circ+1

Agar ctg\alpha =\frac{1}{8} bo‘lsa, \frac{\sin 2a + 2\sin^2a}{\sin 2a + 2\cos^2\alpha } ni hisoblang.

Hisoblang. \sin 10^\circ\cdot \sin 30^\circ\cdot \sin 50^\circ\cdot \sin 70^\circ

Hisoblang. cos20^\circ\cdot cos40^\circ\cdot cos80^\circ

Hisoblang. \cos \frac{\pi }{5}\cdot \cos \frac{2\pi }{5}

Hisoblang. \frac{sin36^\circ}{\sin 12^\circ}-\frac{\cos 36^\circ}{\cos 12^\circ}=?

Hisoblang. \frac{2tg(240^\circ)}{1-tg^{2}(240^\circ)}

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

Soddalashtiring. \frac{2}{tg\alpha + ctg\alpha }

Soddalashtiring. \frac{2}{ctg\alpha - tg\alpha }

Hisoblang. \sin ^{4}(\frac{23\pi }{12})-\cos ^{4}(\frac{13\pi }{12})

Quyidagi keltirilgan ifodalardan qaysi birining qiymati 1 ga teng emas?

1) 2 \cos^{2}\alpha - \cos 2\alpha; 

2) 2 \sin^{2}\alpha + \cos 2\alpha;

3) tg(90^\circ+\alpha )tg\alpha;

4) (\frac{1}{cos^{2}\alpha }-1)(\frac{1}{\sin^{2}\alpha }-1)

(3 va 4 ifodalar \alpha ning qabul qilishi mumkin bo‘lgan qiymatlarida qaraladi.)

Hisoblang. \frac{\sqrt{3}}{\sin 100^\circ}+\frac{1}{\cos 260^\circ}

Soddalashtiring. \sin ^{6}\alpha + \cos ^{6}\alpha + \frac{3}{4}\sin^{2}2\alpha

Hisoblang. 14\sqrt{2}(\sin ^{4}(\frac{3\pi }{8})-\cos ^{4}(\frac{3\pi }{8}))

\sin ^{4}\alpha +\cos ^{4}\alpha ning eng kichik qiymatini toping.

\sin 150^\circ ning qiymati \cos 20^\circ \cdot \cos 40^\circ \cdot \cos 80^\circ ning qiymatidan qanchaga katta?

Hisoblang. \log _{2}\cos 20^\circ +\log _{2}\cos 40^\circ +\log _{2}\cos 60^\circ +\log _{2}\cos 80^\circ

Agar tg\alpha +ctg\alpha =4 bo‘lsa, \sin 2\alpha ni hisoblang.

Ifodaning qiymatini hisoblang. \frac{1}{\sin 10^\circ}-\frac{\sqrt{3}}{\cos 10^\circ}