====== Question 1, Review Exercise ======
Solutions of Question 1 of Review Exercise of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 

=====Question 1=====
Select the correct option in the following.\\

i.   $\sin \left(45^{\circ}-30^{\circ}\right)=\ldots$\\
    * (a) $\frac{\sqrt{6}-\sqrt{2}}{4}$\\ 
    * (b) $\frac{\sqrt{6}+\sqrt{2}}{4}$\\
    * %%(c)%% $\frac{\sqrt{6}-\sqrt{2}}{2}$\\
    * (d) $\frac{\sqrt{3}-\sqrt{2}}{2}$ \\ <btn type="link" collapse="a1">See Answer</btn><collapse id="a1" collapsed="true">%%(a)%%: $\frac{\sqrt{6}-\sqrt{2}}{4}$ </collapse>

ii. $\tan \left(\frac{\pi}{6}+\frac{\pi}{4}\right)=\ldots$\\
    * (a) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$\\ 
    * (b) $\frac{\sqrt{3}+1}{\sqrt{3}-1}$\\
    * %%(c)%% $\frac{\sqrt{3}+1}{-\sqrt{3}-1}$\\
    * (d) $\frac{\sqrt{3}+1}{-\sqrt{3}+1}$ \\ <btn type="link" collapse="a2">See Answer</btn><collapse id="a2" collapsed="true">(b): $\frac{\sqrt{3}+1}{\sqrt{3}-1}$</collapse>

iii. $\sin 22.5^{\circ} \cos 22.5^{\circ}+\cos 22.5^{\circ} \sin 22.5^{\circ}=\ldots$\\  
    * (a) $\frac{-1}{\sqrt{3}}$\\
    * (b)$\frac{1}{\sqrt{3}}$\\
    * %%(c)%% $\frac{1}{\sqrt{2}}$\\
    * (d) $\frac{-1}{\sqrt{2}}$\\ <btn type="link" collapse="a3">See Answer</btn><collapse id="a3" collapsed="true">(c): $\frac{1}{\sqrt{2}}$</collapse>

iv. $\cos (\pi-\theta)=\ldots$\\
    * (a) $\sec \theta$\\
    * (b) $\pm \cos \theta$\\
    * %%(c)%% $\cos \theta$\\
    * (d) $-\cos \theta$\\ <btn type="link" collapse="a4">See Answer</btn><collapse id="a4" collapsed="true">(d):$-\cos \theta$ </collapse>

v. $\tan \left(\frac{\pi}{2}+\theta\right)=\ldots$\\
    * (a) $\cot \theta$\\
    * (b) $-\cot \theta$\\
    * %%(c)%% $\tan \theta$\\
    * (d) $-\tan \theta$\\ <btn type="link" collapse="a5">See Answer</btn><collapse id="a5" collapsed="true">(b): $-\cot \theta$</collapse>

vi.  $2 \sin \alpha \cos \alpha=\ldots$\\
    * (a) $\sin (\pi-2 \alpha)$\\
    * (b) $\sin (\pi+2 \alpha)$\\
    * %%(c)%% $\sin (-2 \alpha)$\\
    * (d) $\sin 2(\pi-\alpha)$\\ <btn type="link" collapse="a6">See Answer</btn><collapse id="a6" collapsed="true">(a): $\sin (\pi-2 \alpha)$</collapse>

vii.  $\frac{\sin 2 \alpha \cos \alpha}{\cos ^{3} \alpha-\cos \alpha \sin ^{2} \alpha}=\ldots$\\
    * (a) $\csc 2 \alpha$\\
    * (b) $-\sec 2 \alpha$\\
    * %%(c)%% $\tan 2 \alpha$\\
    * (d) $\tan 2 \alpha$\\ <btn type="link" collapse="a7">See Answer</btn><collapse id="a7" collapsed="true">%%(c)%%: $\tan 2 \alpha$</collapse>

viii. If $\sin \beta=\frac{3}{5}$, then $\cos 2 \beta=\ldots$\\
    * (a) $\frac{-7}{5}$\\ 
    * (b) $\frac{7}{5}$\\
    * %%(c)%% $\frac{-7}{25}$\\
    * (d) $\frac{7}{25}$\\ <btn type="link" collapse="a8">See Answer</btn><collapse id="a8" collapsed="true">%%(d)%%: $\frac{7}{25}$</collapse>

ix. $\cos ^{2} 3 x-\sin ^{2} 3 x=\ldots$\\
    * (a) $\sin 6 x$\\
    * (b) $\cos 6 x$\\
    * %%(c)%% $-\sin 6 x$\\
    * (d) $-\cos 6 x$\\ <btn type="link" collapse="a9">See Answer</btn><collapse id="a9" collapsed="true">%%(b)%%:$\cos 6 x$</collapse>

x.  $(\sin x-\cos x)^{2}=\ldots$\\
    * (a) $1+\sin 2 x$\\
    * (b) $1-\cos 2 x$\\
    * %%(c)%% $1-\sin 2 x$\\
    * (d) $1+\cos \sin 2 x$ \\ <btn type="link" collapse="a10">See Answer</btn><collapse id="a10" collapsed="true">%%(c)%%: $1-\sin 2 x$</collapse>

xi.  $\cos \left(60^{\circ}-30^{\circ}\right) \neq \ldots$\\
    * (a) $\cos 30^{\circ}$\\
    * (b) $\sec 30^{\circ}$\\
    * %%(c)%% $\sqrt{1-\sin ^{2} 30^{\circ}}$\\
    * (d) $\cos 60^{\circ}-\cos 30^{\circ}$\\ <btn type="link" collapse="a11">See Answer</btn><collapse id="a11" collapsed="true">%%(d)%%: $\cos 60^{\circ}-\cos 30^{\circ}$</collapse>

xii.  $\frac{1-\cos x}{\sin x}=\ldots$.\\
    * (a) $\tan \left(\frac{x}{2}\right)$\\
    * (b) $\cot \left(\frac{x}{2}\right)$\\
    * %%(c)%% $-\tan \left(\frac{x}{2}\right)$\\
    * (d) $-\cot \left(\frac{x}{2}\right)$\\ <btn type="link" collapse="a12">See Answer</btn><collapse id="a12" collapsed="true">%%(a)%%: $\tan \left(\frac{x}{2}\right)$</collapse>


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