1. Scenario-2: cosx+cosy=a,sinx+siny=b \cos \mathrm{x}+\cos \mathrm{y}=\mathrm{a}, \sin \mathrm{x}+\sin \mathrm{y}=\mathrm{b} cosx+cosy=a,sinx+siny=b.
Express tan3θ \tan 3 \theta tan3θ by the help of tanθ \tan \theta tanθ.
According to the scenario-2, express the value of cos(x+y) \cos (x+y) cos(x+y) in terms of a a a and b b b.
According to the scenario-1, prove that, BCcosC−BCcosB=(AC−AB)(1+cosA) B C \cos C-B C \cos B=(A C-A B)(1+\cos A) BCcosC−BCcosB=(AC−AB)(1+cosA).
2.
Find the coordinate of the point of intersection of ABABAB \mathrm{AB} AB and yyy y y-axis.
Find the equation of straight line which passes through the point P \mathrm{P} P and makes an angle 45∘ 45^{\circ} 45∘ with AB. \mathrm{AB} .AB.
Find the equation of straight lines which are perpendicular to AB \mathrm{AB} AB and at a distance 2 units from P \mathrm{P} P.
3. Scenario-1: x+y+z=1x+2y+z=2x+y+2z=0 \begin{array}{l} \text { Scenario-1: } x+y+z=1 \\ x+2 y+z=2 \\ x+y+2 z=0 \end{array} Scenario-1: x+y+z=1x+2y+z=2x+y+2z=0
Scenario-2: D=8∣p−q−r2ppqq−r−p2qrrr−p−q2∣ D=8\left|\begin{array}{ccc}\frac{p-q-r}{2} & p & p \\ q & \frac{q-r-p}{2} & q \\ r & r & \frac{r-p-q}{2}\end{array}\right| D=82p−q−rqrp2q−r−prpq2r−p−q
If A=[123] A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right] A=[123] and B=[321] B=\left[\begin{array}{l}3 \\ 2 \\ 1\end{array}\right] B=321, then find (AB)1 (A B)^{1} (AB)1.
Solve the system of linear equations in scenario-1 through determinant.
From scenario-2, prove that, D=S3 D=S^{3} D=S3, where S=p+q+r S=p+q+r S=p+q+r
4.
Find the value of cos2θ \cos 2 \theta cos2θ where cotθ=2 \cot \theta=\sqrt{2} cotθ=2.
Show that, 34cosecA−14secA=1 \frac{\sqrt{3}}{4} \operatorname{cosec} A-\frac{1}{4} \sec A=1 43cosecA−41secA=1 according to the stem.
Using stem, show that, 3−cos2(θ+A)−cos2A−cos2(θ−A)=32 3-\cos ^{2}(\theta+A)-\cos ^{2} A-\cos ^{2}(\theta-A)=\frac{3}{2} 3−cos2(θ+A)−cos2A−cos2(θ−A)=23.
5. Scenario-1: g(x)=sinx g(x)=\sin x g(x)=sinx
Scenario-2: x=tan2y x=\tan \sqrt{2 y} x=tan2y
Find the derivative of logxa \log _{x} a logxa with respect to x x x.
Find the extreme value of 1+2g(x)+3[1−{g(x)}2] 1+2 g(x)+3\left[1-\{g(x)\}^{2}\right] 1+2g(x)+3[1−{g(x)}2] with interval 0≤x≤π2 0 \leq x \leq \frac{\pi}{2} 0≤x≤2π according to the scenario-1.
Prove that, (1+x2)2y2+2(1+x2)xy1=1 \left(1+x^{2}\right)^{2} y_{2}+2\left(1+x^{2}\right) x y_{1}=1 (1+x2)2y2+2(1+x2)xy1=1 according to the scenario-2
Scenario-2: 
