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.

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>

  (a): $\frac{\sqrt{6}-\sqrt{2}}{4}$

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>

  (b): $\frac{\sqrt{3}+1}{\sqrt{3}-1}$

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>

  ©: $\frac{1}{\sqrt{2}}$

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>

  (d):$-\cos \theta$

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>

  (b): $-\cot \theta$

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>

  (a): $\sin (\pi-2 \alpha)$

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>

  (c): $\tan 2 \alpha$

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>

  (d): $\frac{7}{25}$

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>

  (b):$\cos 6 x$

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>

  (c): $1-\sin 2 x$

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>

  (d): $\cos 60^{\circ}-\cos 30^{\circ}$

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>

  (a): $\tan \left(\frac{x}{2}\right)$

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