Question 1 :
If $16\cot \theta = 12$, then $\dfrac {\sin \theta - \cos \theta}{\sin \theta + \cos \theta} = $ _____

Question 3 :
If $\cos x + \sec x = - 2$ for a positive odd integer $n$ then $\cos^nx + \sec^nx$ is

Question 4 :
If $\displaystyle \sin \theta+\sin ^{2} \theta +\sin ^{3}\theta= 1$ then the value of $\displaystyle \cos ^{6}\theta-4\cos ^{4}\theta+8\cos ^{2}\theta$ equals<br/>

Question 5 :
In $\displaystyle A_{n}=\cos^{n}\theta+\sin^{n}\theta, n\in N$ and $\displaystyle \theta \in R$<br/><br/>If $\displaystyle A_{n-4}-A_{n-2}=\sin^{2}\theta\cos^{2}\theta A_{\lambda} $ , then $\displaystyle \lambda $ equals<br/>

Question 7 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then

Question 8 :
For all real values of $\theta$ , $\cot\theta-2 \cot 2\theta$ is equal to

Question 9 :
If $a=\cos\alpha \cos\beta+\sin \alpha \sin\beta \cos\gamma$<br/>$b=\cos\alpha \sin \beta-\sin\alpha \cos\beta \cos\gamma$<br/>and $c=\sin \alpha \sin\gamma$, then $a^2+b^2+c^2$ is equal to

Question 11 :
Let $x=(1+\sin A)(1-\sin B)(1+\sin C), y=(1-\sin A)(1-\sin B)(1-\sin C)$ and if $x=y$, then

Question 13 :
If $0\leq x, y\leq 180^o$ and $\sin (x-y)=\cos(x+y)=\dfrac 12$, then the values of $x$ and $y$ are given by

Question 14 :
In atriangle $ABC$, $\sin A\cos B=\dfrac{1}{4}$ and $3\tan A=\tan B$ , the triangle is

Question 15 :
$1)$ lf $\mathrm{x}$ lies in the lst quadrant and<br/>$\cos \mathrm{x}+\cos 3\mathrm{x}=\cos 2\mathrm{x}$ then $\mathrm{x}=30^{\mathrm{o}}$ or $45^{\mathrm{o}}$<br/>$2)\mathrm{x}\in(0,2\pi)$ and cosec $\mathrm{x}+2=0$ then $x=\displaystyle \frac{7\pi}{6},\frac{l1\pi}{6}$<br/>$3)\mathrm{x}\in[0,2\pi]$ and $(2 \cos \mathrm{x}- \mathrm{l}) (3+2\cos \mathrm{x})=0$ then $\displaystyle \mathrm{x}=\frac{\pi}{3}$ , $\displaystyle \frac{5\pi}{3}$ Which of the above statements are correct?<br/>