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) $\frac{\sqrt{3}-\sqrt{2}}{2}$
    See Answer
    (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) $\frac{\sqrt{3}+1}{-\sqrt{3}+1}$
    See Answer
    (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) $\frac{-1}{\sqrt{2}}$
    See Answer
    ©: $\frac{1}{\sqrt{2}}$

iv. $\cos (\pi-\theta)=\ldots$

  • (a) $\sec \theta$
  • (b) $\pm \cos \theta$
  • (c) $\cos \theta$
  • (d) $-\cos \theta$
    See Answer
    (d):$-\cos \theta$

v. $\tan \left(\frac{\pi}{2}+\theta\right)=\ldots$

  • (a) $\cot \theta$
  • (b) $-\cot \theta$
  • (c) $\tan \theta$
  • (d) $-\tan \theta$
    See Answer
    (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) $\sin 2(\pi-\alpha)$
    See Answer
    (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) $\tan 2 \alpha$
    See Answer
    (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) $\frac{7}{25}$
    See Answer
    (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) $-\cos 6 x$
    See Answer
    (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) $1+\cos \sin 2 x$
    See Answer
    (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) $\cos 60^{\circ}-\cos 30^{\circ}$
    See Answer
    (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) $-\cot \left(\frac{x}{2}\right)$
    See Answer
    (a): $\tan \left(\frac{x}{2}\right)$

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