Qo‘shish formulalari mavzusidan test savollari

((tg^2\frac{7\pi }{24}-tg^2\frac{\pi }{24}):(1-tg^2\frac{7\pi }{24}\cdot tg^2\frac{\pi }{24}))^{2} ni hisoblang.

4cos20^\circ - \sqrt{3}ctg20^\circ ni hisoblang.

(tg60^\circ cos15^\circ - sin15^\circ) \cdot 7\sqrt{2} ning qiymatini toping.

\begin{cases}\sin{x}\cdot \cos{y}=-\frac{1}{3} \\ \cos{x}\cdot \sin{y}=\frac{2}{3} \end{cases} tenglamadan ctg(x-y) ning qiymatini toping.

Agar sin\alpha = -\frac{1}{3} va cos\beta =-\frac{1}{2} bo‘lsa, sin(\alpha +\beta )\cdot sin(\alpha -\beta ) ning qiymatini hisoblang.

Agar tg\alpha = 3, tg\beta =-\frac{1}{2}, 0<\alpha<\pi va \frac{\pi}{2}<\beta<0 bo‘lsa, \alpha+\beta ni toping.

\frac{2cos(\frac{\pi }{4}-\alpha )+\sqrt{2}\sin (\frac{3\pi }{2}-\alpha )}{2sin(\frac{2\pi }{3}+\alpha )-\sqrt{3}\cos (2\pi -\alpha )} ni soddalashtiring.

\alpha ,\beta ,\gamma o‘tkir burchaklar bo‘lib, tg\alpha =\frac{1 }{2},tg\beta = \frac{1}{5} va tg\gamma = \frac{7}{9} bo‘lsa, \gamma ni \alpha va \beta lar orqali ifodalang.

Soddalashtiring: \frac{sin{\alpha+cos{\alpha}}}{\sqrt{2}cos{\frac{\pi}{4}-{\alpha}}}

Hisoblang: cos15^\circ + \sqrt{3}sin15^\circ

Agar sin\alpha = -\frac{1}{3} va cos\beta = -\frac{1}{2} bo‘lsa, sin(\alpha +\beta )\cdot sin(\alpha -\beta ) ning qiymatini toping.

Soddalashtiring: \frac{cos18^\circ \cdot cos28^\circ + cos108^\circ \cdot sin208^\circ}{sin18^\circ \cdot sin78^\circ + sin108^\circ \cdot sin168^\circ}

Soddalashtiring: \frac{sin56^\circ \cdot sin124^\circ - sm34^\circ \cdot cos236^\circ}{cos28^\circ \cdot sin88^\circ + sin178^\circ \cdot cos242^\circ}

Soddalashtiring: \frac{cos{18^\circ}{\cdot} cos{28^\circ} + cos{108^\circ}{\cdot} sin{208^\circ}}{sin{34^\circ}{\cdot}sin{146^\circ}+sin{236^\circ}{\cdot}sin{304^\circ}}

Ifodani soddalashtiring: \frac{cos(\alpha +\beta ) + 2sin\alpha \cdot sin\beta }{\sin (\alpha +\beta )-2cos\beta \cdot sin\alpha }

Soddalashtiring: \frac{sin{56^\circ}{\cdot}sin{124^\circ}-sin{34^\circ}{\cdot}cos{236^\circ}}{cos{28^\circ}{\cdot}cos{88^\circ}+cos{78^\circ}{\cdot}sin{208^\circ}}

\begin{cases}\cos{x}\cdot \cos{y} = \frac{1}{6} \\ {tgx\cdot tgy=2} \end{cases} tenglamadan \cos(x + y) ning qiymatini toping

\begin{cases}sinx\cdot siny=\frac{1}{4}\\ ctgx\cdot ctgy=3\end{cases} tenglama yordamida cos(x-y)ni toping:

Agar sin\alpha \cdot sin\beta = 1 va sin\beta \cdot cos\alpha =\frac{ 1}{2} bo‘lsa, \alpha -\beta ning qiymatlarini toping.

Agar \begin{cases}sin^{2}x=cosx\cdot cosy \\cos^{2}x=sinx\cdot siny \end{cases} bo‘lsa, cos(x-y) ni toping?

Soddalashtiring: ctg2a - ctga

Quyidagi sonlardan qaysi biri qolgan uchtasiga teng emas?

p=\frac{1}{sin^{2}x}-ctg^{2}x, 

q = tgx\cdot tg(270^\circ - x), (x\ne \frac{\pi k}{2},k\in Z),

r = cos^{2}(270^\circ - x) + cos^{2}x,

l= sin42^\circ\cdot cos48^\circ + sin48^\circ\cdot cos42^\circ

Agar \alpha ,\beta \in (0;\frac{\pi }{2}) va (tg\alpha +\sqrt{3})\cdot (tg\beta +\sqrt{3})=4 bo‘lsa, 9\cdot (\frac{\alpha +\beta }{\pi })^{2} ning qiymatini toping.

Agar tg\alpha + tg\beta =\frac{5}{6} va tg\alpha \cdot tg\beta = \frac{1}{6} bo‘lsa, \alpha +\beta nimaga teng bo‘ladi?

Agar \alpha =-45^\circ va \beta = 15^\circ bo‘lsa, cos(\alpha +\beta ) + 2sin\alpha \cdot sin\beta ning qiymatini toping.

Agar tg(\alpha -\beta )=5 va \alpha = 45^\circ bo‘lsa, tg\beta ning qiymatini toping.

Agar \alpha ,\beta \in (0;\frac{\pi }{2}) va (tg\alpha +1)(tg\beta +1)=2 bo‘lsa, 3.2(\frac{\alpha +\beta }{\pi })^{2} ning qiymati nimaga teng?

Quyidagi tengliklardan qaysi biri noto‘g‘ri?

Agar sin\alpha =\frac{3}{5}, sin\beta =\frac{5}{13}, \frac{\pi }{2}<\alpha<\pi, \frac{\pi }{2}<\beta<\pi, bo‘lsa, sin(\alpha-\beta) ning qiymati qanchaga teng.

Agar 5x^{2} - 3x - 1 = 0 tenglamaning ildizlari tg\alpha va tg\beta bo‘lsa, tg(\alpha +\beta ) qanchaga teng bo‘ladi?