SSC CGL MATHS QUIZ

If $3 \cos ^{2} \theta-4 \sin \theta+1=0, \tan \theta+\sec \theta=?$

IF $\cos (x+y)=\sin (2 x-y)$, then the value of $\tan ^{2} x$ is.

IF $A=30^{\circ}, B=60^{\circ}$ and $C=135^{\circ}$, then what is the value of $\sin ^{3} A+\cos ^{3} B+\tan ^{3} C-$ $3 \sin A \cos B \tan C$.

IF $5 \sin ^{2} \theta+14 \cos \theta=13,0^{\circ}<\theta<90^{\circ}$, then what is the value of $\frac{\sec \theta+\cot \theta}{\operatorname{cosec} \theta+\tan \theta} $.

In a triangle $\mathrm{ABC}, \mathrm{AC}=8 \mathrm{~cm}, \mathrm{AB}=6 \mathrm{~cm}$, and $\mathrm{BC}=12 \mathrm{~cm}$ then find the value of $\angle \mathrm{ACB}$ $=?$

Two sides of triangle is $10 \mathrm{~cm}$ and $20 \mathrm{~cm}$ area is $80 \mathrm{~cm}^{2}$. Find the third side.

In a $\triangle \mathrm{ABC}, \mathrm{AD}$ divides $\mathrm{BC}$ in the ratio $2: 3$, $\angle \mathrm{B}=30^{\circ}, \angle \mathrm{C}=45^{\circ} .$ Find $\frac{\sin \angle \mathrm{BAD}}{\sin \angle \mathrm{CAD}} .$

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of sides of a triangle is.

If $3 \sec ^2 \theta+\tan \theta-7=0 \\\ and \\\ 0^{\circ}<\theta<90^{\circ}$, then what is the value of $\left(\frac{2 \sin \theta+3 \cos \theta}{\operatorname{cosec} \theta+\sec \theta}\right) ?$

If $\sin \theta+\cos \theta=\frac{\sqrt{5}}{2}$ , then  Find the value of  $\sin ^{6} \theta+\cos ^{6} \theta+$ $5 \sin ^{2} \theta \cdot \cos ^{2} \theta$ .